A priori estimates and existence for a class of fully nonlinear elliptic equations in conformal geometry

Xu Jia Wang

doi:10.1007/s11401-005-0529-6

A priori estimates and existence for a class of fully nonlinear elliptic equations in conformal geometry

Xu Jia Wang^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

32 Citations (Scopus)

Abstract

In this paper we prove the interior gradient and second derivative estimates for a class of fully nonlinear elliptic equations determined by symmetric functions of eigenvalues of the Ricci or Schouten tensors. As an application we prove the existence of solutions to the equations when the manifold is locally conformally flat or the Ricci curvature is positive.

Original language	English
Pages (from-to)	169-178
Number of pages	10
Journal	Chinese Annals of Mathematics. Series B
Volume	27
Issue number	2
DOIs	https://doi.org/10.1007/s11401-005-0529-6
Publication status	Published - Apr 2006

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title = "A priori estimates and existence for a class of fully nonlinear elliptic equations in conformal geometry",

abstract = "In this paper we prove the interior gradient and second derivative estimates for a class of fully nonlinear elliptic equations determined by symmetric functions of eigenvalues of the Ricci or Schouten tensors. As an application we prove the existence of solutions to the equations when the manifold is locally conformally flat or the Ricci curvature is positive.",

keywords = "Conformal geometry, Elliptic equation, Ricci curvature",

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AB - In this paper we prove the interior gradient and second derivative estimates for a class of fully nonlinear elliptic equations determined by symmetric functions of eigenvalues of the Ricci or Schouten tensors. As an application we prove the existence of solutions to the equations when the manifold is locally conformally flat or the Ricci curvature is positive.

KW - Conformal geometry

KW - Elliptic equation

KW - Ricci curvature

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JO - Chinese Annals of Mathematics. Series B

JF - Chinese Annals of Mathematics. Series B

IS - 2

ER -

A priori estimates and existence for a class of fully nonlinear elliptic equations in conformal geometry

Abstract

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