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- Yamabe_problem abstract "The Yamabe problem in differential geometry concerns the existence of Riemannian metrics with constant scalar curvature, and takes its name from the mathematician Hidehiko Yamabe. Although Yamabe (1960) claimed to have a solution in 1960, which was less than a year before his death, a critical errorin his proof was discovered by Trudinger (1968). The combined work of Neil Trudinger, Thierry Aubin, and Richard Schoen provided a complete solution to the problem as of 1984.The Yamabe problem is the following: given a smooth, compact manifold M of dimension n ≥ 3 with a Riemannian metric g, does there exist a metric g<div/>' conformal to g for which the scalar curvature of g<div/>' is constant? In other words, does a smooth function f exist on M for whichthe metric g<div/>' = e2fg has constant scalar curvature? The answer is now known to be yes, and was proved using techniques from differential geometry, functional analysis and partial differential equations.".
- Yamabe_problem wikiPageExternalLink 1200689814.
- Yamabe_problem wikiPageExternalLink item?id=ASNSP_1968_3_22_2_265_0.
- Yamabe_problem wikiPageID "11757994".
- Yamabe_problem wikiPageRevisionID "591599883".
- Yamabe_problem hasPhotoCollection Yamabe_problem.
- Yamabe_problem subject Category:Mathematical_problems.
- Yamabe_problem subject Category:Riemannian_geometry.
- Yamabe_problem type Abstraction100002137.
- Yamabe_problem type Attribute100024264.
- Yamabe_problem type Condition113920835.
- Yamabe_problem type Difficulty114408086.
- Yamabe_problem type MathematicalProblems.
- Yamabe_problem type Problem114410605.
- Yamabe_problem type State100024720.
- Yamabe_problem comment "The Yamabe problem in differential geometry concerns the existence of Riemannian metrics with constant scalar curvature, and takes its name from the mathematician Hidehiko Yamabe. Although Yamabe (1960) claimed to have a solution in 1960, which was less than a year before his death, a critical errorin his proof was discovered by Trudinger (1968).".
- Yamabe_problem label "Problème de Yamabe".
- Yamabe_problem label "Yamabe problem".
- Yamabe_problem label "山邊問題".
- Yamabe_problem sameAs Problème_de_Yamabe.
- Yamabe_problem sameAs m.02rr9l2.
- Yamabe_problem sameAs Q3406245.
- Yamabe_problem sameAs Q3406245.
- Yamabe_problem sameAs Yamabe_problem.
- Yamabe_problem wasDerivedFrom Yamabe_problem?oldid=591599883.
- Yamabe_problem isPrimaryTopicOf Yamabe_problem.