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.

Cited by in corpus (3)

• Poincaré- and Sobolev- type inequalities for complex $m$-Hessian equations
• The classification of holomorphic $(m,n)$--subharmonic morphisms
• Subextension and approximation of $m$-subharmonic functions with given boundary values