Convexity and singularities of curvature equations in conformal geometry

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We define a generalization of convex functions, which we call $δ$-convex functions, and show they must satisfy interior Hölder and $W^{1,p}$ estimates. As an application, we consider solutions of a certain class of fully nonlinear equations in conformal geometry with isolated singularities, in the case of non-negative Ricci curvature. We prove that such solutions either extend to a Hölder continuous function across the singularity, or else have the same singular behavior as the fundamental solution of the conformal Laplacian. We also obtain various removable singularity theorems for these equations.
35 pages; final version published in IMRN

Keywords

Differential Geometry, Analysis of PDEs

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/101173

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0504066
 http://arxiv.org/abs/math/0504066
 Int. Math. Res. Not. 2006, Art. ID 96890

Collections

arXiv