p-Laplace Equations, p-Superharmonic Functions, and Applications in Conformal Geometry

Abstract

In this paper, we give an exposition of our recent work on nonlinear potential theory in conformal geometry. We apply nonlinear potential theory to study p-Laplace equations arising from conformal geometry and, in particular, the problems related to the asymptotic behavior near and the size of singularities in conformal geometry.

Keywords

p-Laplace equations / p-superharmonic functions / Wolff potentials / p-capacities / p-thin sets for singular behavior / intermediate Schouten curvature tensor / Hausdorff dimensions