The Geometry of m-Hyperconvex Domains.

Abstract

We study the geometry of m-regular domains within the Caffarelli-Nirenberg-Spruck model in terms of barrier functions, envelopes, exhaustion functions, and Jensen measures. We prove among other things that every m-hyperconvex domain admits an exhaustion function that is negative, smooth, strictly m-subharmonic, and has bounded m-Hessian measure.