Classification of singularities for a subcritical fully nonlinear problem

María del Mar González

Vol. 226 (2006), No. 1, 83–102

DOI: 10.2140/pjm.2006.226.83

Abstract

We study isolated singularities for a fully nonlinear elliptic PDE of subcritical type. This equation appears in conformal geometry when dealing with the k-curvature of a locally conformally-flat manifold. (The k-curvature generalizes scalar curvature.) We give a classification result: either the function is bounded near the singularity, or it has a specific asymptotic behavior.

Keywords

subcritical problem, curvature equation, classification of singularities

Mathematical Subject Classification 2000

Primary: 35J60, 53A30

Milestones

Received: 25 August 2004

Revised: 24 January 2005

Accepted: 24 January 2005

Published: 1 July 2006