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To find the minimal surface with a given boundary
In mathematics, Plateau's problem is to show the existence of a minimal surface with a given boundary. The problem is considered part of the calculus of
Plateau's_problem
American mathematician (1897–1965)
mathematician and Fields Medalist known for his general solution to Plateau's problem. He was born to a Jewish family in New York City, the son of Sarah
Jesse_Douglas
Belgian physicist (1801–1883)
displays—desktop, mobile, and the Google App. Patterns in nature Plateau's laws Plateau's problem Plateau–Rayleigh instability Soap bubble Stretched grid method
Joseph_Plateau
Mathematics award
Sylvia; Gruber, David (21 August 2006). "Manifold Destiny: A legendary problem and the battle over who solved it". The New Yorker. Archived from the original
Fields_Medal
American mathematician and billionaire (1938–2024)
College Dublin in 2018. Simons, J. (August 1967). "Minimal Cones, Plateau's Problem, and the Bernstein Conjecture". Proc Natl Acad Sci U S A. 58 (2):
Jim_Simons
Interdisciplinary research area
provided the first mathematical characterization of why and when barren plateaus occur in variational quantum algorithms, establishing theoretical guarantees
Quantum_machine_learning
Differential calculus on function spaces
problems for the Laplace equation satisfy the Dirichlet's principle. Plateau's problem requires finding a surface of minimal area that spans a given contour
Calculus_of_variations
American mathematician (1933–1997)
1951), and proposed them as generalized solutions to Plateau's problem in order to deal with the problem even when a concept of orientation is missing. He
Frederick_J._Almgren_Jr.
Study of geometric properties of sets through measure theory
measure theory was born out of the desire to solve Plateau's problem (named after Joseph Plateau) which asks if for every smooth closed curve in R 3
Geometric_measure_theory
Problem in differential geometry
In differential geometry, Bernstein's problem is as follows: if the graph of a function on Rn−1 is a minimal surface in Rn, does this imply that the function
Bernstein's_problem
portion of Plateau's problem" but the stationary varifolds used in this section can only solve a greatly simplified version of the problem. For example
Varifold
Topics referred to by the same term
Plateau or plateaux or plateaus may also refer to: Dissected plateau, a highly eroded plateau which may have sharp relief Oceanic plateau, a submarine area
Plateau_(disambiguation)
Periodic minimal surface
surfaces were generated using symmetry arguments: given a solution to Plateau's problem for a polygon, reflections of the surface across the boundary lines
Schwarz_minimal_surface
Russian mathematician
Topological variational problems. – Gordon and Breach, 1991. A.T. Fomenko, Dao Chong Thi Minimal surfaces and Plateau problem. USA, American Mathematical
Anatoly_Fomenko
Relatively flat submarine region that rises well above the level of the ambient seabed
and New Zealand contains the greatest number of oceanic plateaus (see map). Oceanic plateaus produced by large igneous provinces are often associated
Oceanic_plateau
Chinese-American mathematician (born 1949)
They proved that negativity of the mass would allow one to invoke the Plateau problem to construct stable minimal surfaces which are geodesically complete
Shing-Tung_Yau
German journalist and writer (1894–1982)
the mother of mathematician Ernst Robert Reifenberg, who solved a Plateau’s problem. Elise Hirschmann was born into a Jewish family in Berlin, 4 March
Gabriele_Tergit
Plateau in Central, South and East Asia
The Tibetan Plateau, also known as the Qinghai–Tibet Plateau, Qingzang Plateau, is a vast elevated plateau located at the intersection of Central, South
Tibetan_Plateau
geometric measure theory. The notion was applied to find solutions to Plateau's problem. In 2001 the notion of an integral current was extended to arbitrary
Flat_convergence
Plateau in southwestern United States
The Colorado Plateau is a physiographic and desert region of the Intermontane Plateaus, roughly centered on the Four Corners region of the Southwestern
Colorado_Plateau
Region in Mexico
the Basin and Range Province, which in turn is part of the Intermontane Plateaus physiographic division. In phytogeography, the Sonoran Desert is within
Mexican_Plateau
Surface that locally minimizes its area
Björling problem was solved using complex methods. The "first golden age" of minimal surfaces began. Schwarz found the solution of the Plateau problem for
Minimal_surface
Problem in combinatorial optimization
The knapsack problem is the following problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine which items
Knapsack_problem
Quantum Mechanics in Neural Networks
gradients. This situation is known as Barren Plateaus, because most of the initial parameters are trapped on a "plateau" of almost zero gradient, which approximates
Quantum_neural_network
Book published in 2016
a Few Remarks, by Peter Constantin Plateau’s Problem, by Jenny Harrison and Harrison Pugh The Unknotting Problem, by Louis Kauffman How Can Cooperative
Open_Problems_in_Mathematics
Highland region in central-southern United States
The majority of these caves are found in the Ozark counties. The Ozark Plateaus aquifer system affects groundwater movement in all areas except the igneous
Ozarks
American mathematician
of variations and continuum mechanics. She has notably worked on Plateau's problem, providing proofs regarding the existence of solutions for boundary
Jenny_Harrison
Physiographic region of the contiguous United States
the Intermontane Plateaus is one of eight physiographic regions of the contiguous United States. The region consists mostly of plateaus and mountain ranges
Intermontane_Plateaus
Differentiable manifold
Complex Plateau problem studied in the article by F. Reese Harvey and H. Blaine Lawson. There is also further work on the Complex Plateau problem by Stephen
CR_manifold
Region in Interior of British Columbia, Canada
the larger Northern Plateaus province, which in turn is part of the Intermontane Plateaus physiographic division. The Interior Plateau is not part of the
Interior_Plateau
Plateau in northern China
form loess under the arid climate. The Loess Plateau is one of the largest and thickest loess plateaus in the world. Its 635,000-square-kilometre (245
Loess_Plateau
surface Morse theory Noether's theorem Path integral formulation Plateau's problem Prime geodesic Principle of least action Soap bubble Soap film Tautochrone
List_of_variational_topics
Hungarian mathematician (1895–1965)
Szegediensis, 1925 The problem of least area and the problem of Plateau, Mathematische Zeitschrift Vol. 32, 1930, p.763 On the problem of Plateau, Springer-Verlag
Tibor_Radó
Concept in potential theory
method in the calculus of variations. Dirichlet problem Hilbert's twentieth problem Plateau's problem Green's first identity Monna 1975, p. 33 Monna 1975
Dirichlet's_principle
Plateau in India
The Deccan Plateau (/ˈdɛkən/ DEK-ən ) or Peninsular Plateau, is a plateau that extends over an area of 422,000 km2 (163,000 sq mi) on the southern part
Deccan_Plateau
Topics referred to by the same term
Minification (disambiguation) Maximisation (disambiguation) Magnification Plateau's problem This disambiguation page lists articles associated with the title
Minimisation
Mathematician
flows in Euclidean space and in Minkowski space, and to the asymptotic Plateau problem for constant-curvature hypersurfaces in hyperbolic space". "Ling Xiao"
Ling_Xiao
Motivating example in mathematical study
obstacle problem is a classic motivating example in the mathematical study of variational inequalities and free boundary problems. The problem is to find
Obstacle_problem
Mathematical formulation of special and general relativity
Lagrangian system Non-autonomous mechanics Restricted three-body problem Plateau's problem The line element squared is the Lorentz invariant c 2 d τ 2 =
Relativistic Lagrangian mechanics
Relativistic_Lagrangian_mechanics
fluid films form surfaces of minimal surface area, leading to the Plateau problem. On the other hand, fluid films display rich dynamic properties. They
Dynamic_fluid_film_equations
Mountain range in Tamil Nadu, India
Sirumalai (Tamil: சிறுமலை) is a massif region of 60,000 acres (200 km2) situated in Dindigul District, Tamil Nadu, India. Located 25 km (16 mi) from Dindigul
Sirumalai
Formulation of classical mechanics
Lagrangian point Lagrangian system Non-autonomous mechanics Plateau's problem Restricted three-body problem Sometimes in this context the variational derivative
Lagrangian_mechanics
Hypothetical invisible cosmic material
Unsolved problem in physics What is dark matter? How was it generated? More unsolved problems in physics In astronomy and cosmology, dark matter is an
Dark_matter
American mathematician
to exist. Such submanifolds (given as graphs) might not solve the Plateau problem, as they must in the case of graphical hypersurfaces of Euclidean space
Robert_Osserman
French mathematician (1875–1941)
area and applicable surfaces. The final chapter deals mainly with Plateau's problem. This dissertation is considered to be one of the finest ever written
Henri_Lebesgue
Zin-Maung-Maung-Thein; Khin Zaw (June 2021). "Parachute research is another ethical problem for Myanmar amber". Nature Ecology & Evolution. 5 (6): 707. Bibcode:2021NatEE
List_of_lagerstätten
French mathematician
Phong, Duong Hong; Wainger, Stephen, eds. (2014), "Should we solve Plateau's problem again?", Advances in Analysis: The Legacy of Elias M. Stein, Princeton
Guy_David_(mathematician)
Taiwanese-American computer scientist
flow problems included the representation of all pairwise flows using the Gomory–Hu tree,[GH61] the formulation of the multi-commodity flow problem,[H63]
T._C._Hu
American mathematician
co-authored with Wendell Fleming.[FF60] In their work, they showed that Plateau's problem for minimal surfaces can be solved in the class of integral currents
Herbert_Federer
American mathematician
Ph.D. from New York University (NYU). His thesis was entitled The Plateau Problem for Minimal Surfaces of Arbitrary Topological Structure and his thesis
Max_Shiffman
theorem says the Fourier transformation is a unitary operator. Plateau Plateau problem concerns the existence of a minimal surface. plurisubharmonic A
Glossary of real and complex analysis
Glossary_of_real_and_complex_analysis
Italian mathematician (1928–1996)
commentaries from Luis Caffarelli and other noted mathematicians. Plateau's problem Calculus of variations Elliptic partial differential equation Minimal
Ennio_De_Giorgi
Planck's law of black body radiation Joseph Plateau, Belgian physicist – Plateau's laws, Plateau's problem. Plato, Greek philosopher – Platonic solids
List_of_eponyms_(L–Z)
Site of the largest known collection of pyramids, in Egypt
Sayed (2020). "Sustainability problems of the Giza pyramids". Heritage Science. 8: 8. Topographic Map of the Giza Plateau 29°58′34″N 31°07′58″E / 29
Giza_Plateau
Mathematics of smooth surfaces
surface with given boundary exists is called Plateau's problem after the Belgian physicist Joseph Plateau who carried out experiments on soap films in
Differential geometry of surfaces
Differential_geometry_of_surfaces
Minimised surface of liquid connecting two wetted objects
interpretation.) J. Plateau showed the existence of such shapes with given boundaries. The problem was named after him Plateau's problem. Many scientists
Capillary_bridge
Place in Rize, Turkey
positioned below Palovit Plateau, adjacent to the pine groves in the valley descending to Zilkale. It is one of the plateaus that is easier to reach compared
Amlakit_Plateau
American mathematician (1927-1984)
fundamental problems in analysis, among them, the existence of quasiconformal maps, the measurable Riemann mapping theorem, Plateau's problem in the setting
Charles_B._Morrey_Jr.
Vietnamese victory The Troubles Attack on UDR Clogher barracks 2 May Cyprus problem Turkish invasion of Cyprus 20 July—16 August Vietnam War Battle of Thượng
List_of_battles_1901–2000
American mathematician
"Jean Taylor". agnesscott.edu. Retrieved 2014-01-25. Taylor (1976). "Plateau problem | mathematics | Britannica". www.britannica.com. Retrieved 2023-03-01
Jean_Taylor
Discrepancy between past temperatures and the amount of incoming solar radiation
The 100,000-year problem (also 100 ky problem or 100 ka problem) of the Milankovitch theory of orbital forcing refers to a discrepancy between the reconstructed
100,000-year_problem
World Natural Heritage Site in Maharashtra, India
main plateau of Kas has been surveyed in detail by many researchers. The other three plateaus have not been surveyed. The earliest work on the plateau was
Kas_Plateau_Reserved_Forest
Concept in physical cosmology
In physical cosmology, the graceful exit problem refers to an inherent flaw in the initial proposal of the inflationary universe theory proposed by Alan
Graceful_exit_problem
Public higher learning institution in Italy
on the Plateau's problem, on the theory of parametric minimal surfaces, on Lebesgue measure of continuous and related other variational problems: he also
Scuola_Normale_Superiore
Baseline of stellar lithium abundance
The Spite plateau (or Spite lithium plateau) is a minimum abundance of lithium in old stars located in the stellar halo of the Milky Way galaxy, regardless
Spite_plateau
American mathematician (1936–2020)
1007/BF01174896. —— (1980). "Large solutions to the volume constrained plateau problem". Archive for Rational Mechanics and Analysis. 75 (1): 59–77. Bibcode:1980ArRMA
Henry_C._Wente
Natural arch on Gozo, Malta
Bay is characterized by a plateau, with steep cliffs, which slope down into the sea, where there are many caves. On the plateau, artificial salt pans were
Wied_il-Mielaħ_Window
Chinese-Australian mathematician
Neil Trudinger) Trudinger, Neil; Wang, Xu-Jia (2005). "The affine Plateau problem". Journal of the American Mathematical Society. 18 (2): 253–289. doi:10
Xu-Jia_Wang
Group of mountain ranges
covers an extensive area of mountain ranges, intermontane basins, and plateaus in Western and Northwestern Canada, Western United States, and Mexico,
North_American_Cordillera
Italian mathematician (1910–1990)
on the Plateau's problem, on the theory of parametric minimal surfaces, on Lebesgue measure of continuous and related other variational problems: he also
Lamberto_Cesari
Iori Plateau (Georgian: ივრის ზეგანი, ivris zegani), also known as Gare-Kakheti Plateau (გარე კახეთის ზეგანი, gare kakhet'is zegani) is a plateau between
Iori_Plateau
Country in South Asia
in which a set of rules or problems were stated with economy in verse, and a prose commentary that explained the problem in more detail and provided
India
Country in West Asia
landscape is dominated by rugged mountain ranges that separate basins or plateaus. The populous western Iran is the most mountainous, with ranges such as
Iran
Italian mathematician (1940–2024)
(6) 18 (2009), Fascicule Spécial, 59–85. Hilbert's nineteenth problem Plateau's problem "Scheda Personale | DiMaI - Dipartimento di Matematica e Informatica
Enrico_Giusti
Mathematical model or scientific law
are trying to lose weight to experience plateaus after several weeks of successful weight reduction. The plateau principle suggests that this leveling off
Plateau_principle
Geological formation in Nigeria
rule affected the plateau's vegetation. This has resulted in overgrazing and widespread erosion on the plateau and has created problems between the cattle
Mambilla_Plateau
Australian mathematician (born 1945)
(1979). "Boundary regularity and embedded solutions for the oriented Plateau problem". Annals of Mathematics. Second Series. 110 (3): 439–486. doi:10.2307/1971233
Leon_Simon
Species of legume
Significance and is ranked as Australia's worst weed. It is also a major problem in parts of tropical Africa, Hawaii, and other Islands in the Pacific Ocean
Parkinsonia_aculeata
Far-right authoritarian political ideology
Mussolini declared that employment of women was a "major aspect of the thorny problem of unemployment" and that for women, working was "incompatible with childbearing";
Fascism
Country in South America
of tropical and subtropical landscapes, as well as wetlands, savannas, plateaus, and low mountains. It contains most of the Amazon basin, including the
Brazil
German-Jewish mathematician
doctoral dissertation there on partial differential equations and the Plateau problem, in 1910, supervised by H. A. Schwarz. In 1911 he moved to Munich.
Herman_Müntz
Department in Auvergne-Rhône-Alpes, France
the length of the Rhône valley for 140 km and to the west by the high plateaus of the Massif Central. At its widest, the department does not exceed 75 km
Ardèche
American mathematician (born 1945)
Simon: Boundary regularity and embedded solutions of the oriented Plateau problem, Annals of Mathematics, vol. 110, 1979, pp. 439–486. doi:10
Robert_Miller_Hardt
Type of machine learning model
may include filtering out such content. LLM-generated content can pose a problem if the content is similar to human text (making filtering difficult) but
Large_language_model
11965 11966 Plateau 1994 PJ20 Joseph Antoine Ferdinand Plateau (1801–1883) was a Belgian physicist who stated the so-called "Plateau-problem". The proof
Meanings of minor-planet names: 11001–12000
Meanings_of_minor-planet_names:_11001–12000
Problem in astronomy
In astronomy, the lithium problem or lithium discrepancy refers to the discrepancy between the primordial abundance of lithium as inferred from observations
Cosmological_lithium_problem
Optimization algorithm
is an iterative algorithm that starts with an arbitrary solution to a problem, then attempts to find a better solution by making an incremental change
Hill_climbing
current was 3...6 mA, while the reverse grid current reached 1 μA. The problem of TM tubes was their short service life of 100 hours maximum – if the
List_of_vacuum_tubes
Country in South Asia
and plateaus. Pakistan is divided into three major geographic areas: the northern highlands, the Indus River plain, and the Balochistan Plateau. The
Pakistan
Rajasthan Uplands, also known as the Marwar Uplands, form a region of rolling plateaus with rounded hills and forested areas. Located in the western part of the
East_Rajasthan_Uplands
Hypothetical black hole formed soon after the Big Bang
"exotic" inflation models, often featuring inflection points, bumps, or plateaus in the inflaton potential, which can amplify fluctuations by orders of
Primordial_black_hole
considerations of design for cold climates like Buffalo's, and structural problems made themselves apparent almost immediately: the twin steeples were removed
List of churches in the Diocese of Buffalo
List_of_churches_in_the_Diocese_of_Buffalo
Former states in present-day Tanzania (c. 1600–1963)
had some regional development triumphs, but did not deal with the main problem that helped him win the election: the land question. As a result, he lost
Chagga_states
Very large volume eruption of basalt lava
igneous provinces, lava plateaus, and mountain ranges. However, more have been recognized such as the large Ontong Java Plateau, and the Chilcotin Group
Flood_basalt
Tourism in Bosnia and Herzegovina
Blidinje plateau (Croatian: Blidinjska visoravan) is a karst plateau in Bosnia and Herzegovina, situated at the heart of Dinaric Alps, between major mountains
Blidinje_plateau
undergone a rapid tectonic uplift, leading the occurrence of mountain peaks, plateaus, valleys and gorges. Generally speaking the level lands and intermediate
Soil_in_Sa'isi_Tsa'ida_Imba
up the vaccine could prove to be "counterproductive" by creating "other problems like social division and social apartheid" that could "destroy any sense
Timeline of the COVID-19 pandemic in the United Kingdom (January–June 2021)
Timeline_of_the_COVID-19_pandemic_in_the_United_Kingdom_(January–June_2021)
Romance language indigenous to the island of Sardinia
of Orosei, showed that the students of the local middle school had no problem using that standard despite the fact that the Sardinian they spoke was
Sardinian_language
Desert in East Asia
the former at 1,070 to 1,200 m (3,510 to 3,940 ft). The slopes of the plateaus are more or less steep and are sometimes penetrated by "bays" of the lowlands
Gobi_Desert
Mountain range in Asia
to another, and all may be quite different from the weather in nearby plateaus or valleys. The Himalayan hydroclimate is crucial for South Asia, where
Himalayas
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