Journal ArticleDOI
On the existence of a complete Kähler metric on non-compact complex manifolds and the regularity of fefferman's equation
Shiu-Yuen Cheng,Shing-Tung Yau +1 more
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This article is published in Communications on Pure and Applied Mathematics.The article was published on 1980-07-01. It has received 532 citations till now. The article focuses on the topics: Hermitian manifold & Hyperkähler manifold.read more
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Anti De Sitter Space And Holography
TL;DR: In this article, it was shown that the Kaluza-Klein modes of Type IIB supergravity on $AdS_5\times {\bf S}^5$ match with the chiral operators of the super Yang-Mills theory in four dimensions.
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Anti de sitter space and holography
TL;DR: In this article, a correspondence between conformal field theory observables and those of supergravity was proposed, where correlation functions in conformal fields are given by the dependence of the supergravity action on the asymptotic behavior at infinity.
Journal ArticleDOI
the uncertainty principle
TL;DR: In this paper, the authors consider l'existence and the regularite des solutions d'equations aux derivees partielles, the construction de solutions fondamentales explicites and les valeurs propres d'operateurs de Schrodinger.
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Einstein metrics with prescribed conformal infinity on the ball
C. Robin Graham,John M. Lee +1 more
TL;DR: In this article, a boundary problem for Riemannian Einstein metrics is studied, where the conformal class [S] is defined as the conformality of a metric on a compact (n + l)-dimensional manifold with bounding boxes.
References
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BookDOI
Multiple integrals in the calculus of variations
TL;DR: In this paper, a variational method in the theory of harmonic integrals has been proposed to solve the -Neumann problem on strongly pseudo-convex manifolds and parametric Integrals two-dimensional problems.
Journal ArticleDOI
On The Ricci Curvature of a Compact Kahler Manifold and the Complex Monge-Ampere Equation, I*
TL;DR: In this paper, the Ricci form of some Kahler metric is shown to be closed and its cohomology class must represent the first Chern class of M. This conjecture of Calabi can be reduced to a problem in non-linear partial differential equation.
Journal ArticleDOI
Differential equations on riemannian manifolds and their geometric applications
Shiu-Yuen Cheng,Shing-Tung Yau +1 more