Yamabe problem
The Yamabe problem refers to a conjecture in the mathematical field of differential geometry, which was resolved in the 1980s. It is a statement about the scalar curvature of Riemannian manifolds: Let (M,g) be a closed smooth Riemannian manifold. Then there exists a positive and smooth function f on M such that the Riemannian metric fg has constant scalar curvature. By computing a formula for how the scalar curvature of fg relates to that of g, this statement can be rephrased in the following form:
Andrea MalchiodiCR manifoldConformally flat manifoldContributors to the mathematical background for general relativityFernando Codá MarquesGeometric analysisGeometry FestivalHidehiko YamabeJoel SpruckJohn M. LeeJosé F. EscobarList of differential geometry topicsList of incomplete proofsList of nonlinear partial differential equationsLouis NirenbergNeil TrudingerOsaka_UniversityPaneitz operatorPositive energy theoremPrescribed scalar curvature problemRichard SchoenSimon BrendleThierry AubinWeyl–Schouten theoremYamabe flowYamabe invariant
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Yamabe problem
The Yamabe problem refers to a conjecture in the mathematical field of differential geometry, which was resolved in the 1980s. It is a statement about the scalar curvature of Riemannian manifolds: Let (M,g) be a closed smooth Riemannian manifold. Then there exists a positive and smooth function f on M such that the Riemannian metric fg has constant scalar curvature. By computing a formula for how the scalar curvature of fg relates to that of g, this statement can be rephrased in the following form:
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La conjetura de Yamabe es un p ...... ompleta al problema en 1984.
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Le problème de Yamabe en géomé ...... tions aux dérivées partielles.
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O problema de Yamabe, em geome ...... ecebe seu nome do matemático .
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The Yamabe problem refers to a ...... , is not yet fully understood.
@en
Yとアインシュタイン・ヒルベルト汎関数Eを用いて となる。こ ...... て山辺計量の一意性問題は例えば内に制限した場合に意味を持つ。
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Задача Ямабе — вопрос о сущест ...... и опубликовали полное решение.
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Задача Ямабе — питання про існ ...... опублікували повний розв'язок.
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山邊（Yamabe）問題是微分幾何的問題，得名自山邊英彥。雖 ...... 續由、、理查德·舍恩研究，山邊問題在1984年得到完全解決。
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La conjetura de Yamabe es un p ...... ompleta al problema en 1984.
@es
Le problème de Yamabe en géomé ...... tions aux dérivées partielles.
@fr
O problema de Yamabe, em geome ...... ecebe seu nome do matemático .
@pt
The Yamabe problem refers to a ...... phrased in the following form:
@en
Yとアインシュタイン・ヒルベルト汎関数Eを用いて となる。こ ...... て山辺計量の一意性問題は例えば内に制限した場合に意味を持つ。
@ja
Задача Ямабе — вопрос о сущест ...... и опубликовали полное решение.
@ru
Задача Ямабе — питання про існ ...... опублікували повний розв'язок.
@uk
山邊（Yamabe）問題是微分幾何的問題，得名自山邊英彥。雖 ...... 續由、、理查德·舍恩研究，山邊問題在1984年得到完全解決。
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Conjetura de Yamabe
@es
Problema de Yamabe
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Problème de Yamabe
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Yamabe problem
@en
Задача Ямабе
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Задача Ямабе
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山辺問題
@ja
山邊問題
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