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

Xu-Jia Wang

Published 2006-05-23Version 1

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.

Journal: Chinese Annals of Mathematics, 27(B) (2006), 169-178
Categories: math.DG
Subjects: 53A30, 58J05
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