On n-superharmonic functions and some geometric applications

Abstract In this paper we study asymptotic behaviors of n -superharmonic functions at singularity using the Wolff potential and capacity estimates in nonlinear theory. Our results are inspired by extend [6] Arsove–Huber [63] Taliaferro 2 dimensions. To use a new notion thinness terms -capacity motivated type Wiener criterion [6]. [63], employ Adams–Moser–Trudinger’s inequality for potential, which is used [15] Brezis–Merle. For geometric applications, end complete conformally flat manifolds as well properly embedded hypersurfaces hyperbolic space. These applications seem to elevate importance -Laplace equations make closer tie classic analysis developed conformal geometry general