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Geometric analysis is a mathematical discipline where tools from differential equations, especially elliptic partial differential equations (PDEs), are used to establish new results in differential geometry and differential topology. The use of linear elliptic PDEs dates at least as far back as Hodge theory. More recently, it refers largelyto the use of nonlinear partial differential equations to study geometric and topological properties of spaces, such as submanifolds of Euclidean space, Riemannian manifolds, and symplectic manifolds. This approach dates back to the work by Tibor Radó and Jesse Douglas on minimal surfaces, John Forbes Nash Jr. on isometric embeddings of Riemannian manifolds into Euclidean space, work by Louis Nirenberg on the Minkowski problem and the Weyl problem, and w

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rdf:type	sport
rdfs:label	Geometric analysis (en) Analyse géométrique (fr) Análise geométrica (pt)
rdfs:comment	L'analyse géométrique est un champ mathématique à l'interface de la géométrie différentielle et des équations différentielles. (fr) A Análise Geométrica é uma subárea da Matemática na qual se trata de problemas analíticos e geométricos, comumente trata-se problemas das Equações Diferenciais Parciais e da Geometria diferencial. (pt) Geometric analysis is a mathematical discipline where tools from differential equations, especially elliptic partial differential equations (PDEs), are used to establish new results in differential geometry and differential topology. The use of linear elliptic PDEs dates at least as far back as Hodge theory. More recently, it refers largelyto the use of nonlinear partial differential equations to study geometric and topological properties of spaces, such as submanifolds of Euclidean space, Riemannian manifolds, and symplectic manifolds. This approach dates back to the work by Tibor Radó and Jesse Douglas on minimal surfaces, John Forbes Nash Jr. on isometric embeddings of Riemannian manifolds into Euclidean space, work by Louis Nirenberg on the Minkowski problem and the Weyl problem, and w (en)
foaf:depiction
dcterms:subject	Differential geometry Calculus of variations Differential equations
Wikipage page ID	4325474 (xsd:integer)
Wikipage revision ID	1103646235 (xsd:integer)
Link from a Wikipage to another Wikipage	Calculus of variations Variational principle Ricci flow Richard S. Hamilton Richard Schoen Kähler–Einstein metric Pseudoholomorphic curve Differential geometry Mathematics Elliptic partial differential equation Gauge theory (mathematics) Geodesic convexity Clifford Taubes Geometry Submanifold Linear differential equation Louis Nirenberg Embedding Symplectic manifold Mean curvature flow Calculus of variations Tibor Radó Topology Minimal surface Minkowski problem Aleksandr Danilovich Aleksandrov Aleksei Pogorelov American Mathematical Society Euclidean space Partial differential equation Differential equation Differential topology Global analysis Riemannian manifold Grigori Perelman Harmonic map Isometry Hypersurface Differential equations Jesse Douglas John Forbes Nash Jr. Karen Uhlenbeck Hodge theory Differential geometry Manifold Poincaré conjecture Positive energy theorem Shing-Tung Yau Yamabe problem Yang–Mills equations Nonlinear partial differential equations Minimal submanifold
sameAs	Geometric analysis Geometric analysis Geometric analysis Geometric analysis Geometric analysis Geometric analysis Geometric analysis
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Reflist dbt:Industrial_and_applied_mathematics
thumbnail	wiki-commons:Special:FilePath/Saddle_Tower_Minimal_Surfaces.png?width=300
has abstract	Geometric analysis is a mathematical discipline where tools from differential equations, especially elliptic partial differential equations (PDEs), are used to establish new results in differential geometry and differential topology. The use of linear elliptic PDEs dates at least as far back as Hodge theory. More recently, it refers largelyto the use of nonlinear partial differential equations to study geometric and topological properties of spaces, such as submanifolds of Euclidean space, Riemannian manifolds, and symplectic manifolds. This approach dates back to the work by Tibor Radó and Jesse Douglas on minimal surfaces, John Forbes Nash Jr. on isometric embeddings of Riemannian manifolds into Euclidean space, work by Louis Nirenberg on the Minkowski problem and the Weyl problem, and work by Aleksandr Danilovich Aleksandrov and Aleksei Pogorelov on convex hypersurfaces. In the 1980s fundamental contributions by Karen Uhlenbeck, Clifford Taubes, Shing-Tung Yau, Richard Schoen, and Richard Hamilton launched a particularly exciting and productive era of geometric analysis that continues to this day. A celebrated achievement was the solution to the Poincaré conjecture by Grigori Perelman, completing a program initiated and largely carried out by Richard Hamilton. (en) L'analyse géométrique est un champ mathématique à l'interface de la géométrie différentielle et des équations différentielles. (fr) A Análise Geométrica é uma subárea da Matemática na qual se trata de problemas analíticos e geométricos, comumente trata-se problemas das Equações Diferenciais Parciais e da Geometria diferencial. (pt)
gold:hypernym	Discipline
prov:wasDerivedFrom	wikipedia-en:Geometric_analysis?oldid=1103646235&ns=0
page length (characters) of wiki page	4539 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Geometric_analysis
is Link from a Wikipage to another Wikipage of	Ben Andrews (mathematician) David Allen Hoffman Almgren–Pitts min-max theory Huai-Dong Cao Peter Li (mathematician) Ricci flow Richard S. Hamilton Richard Schoen Curvature of Space and Time, with an Introduction to Geometric Analysis Vladimir Markovic Joel Spruck Pengfei Guan Analysis of partial differential equations Mathematical analysis Maximum principle Chikako Mese

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