Lower envelopes with respect to convex subcones of subharmonic and plurisubharmonic functions

Abstract

Let $D$ be a domain in a finite-dimensional Euclidean space, and $H$ be a convex subcone in the convex cone of all subharmonic functions on $D$. We obtain a criterion for the existence of a lower envelope from $H$ for an arbitrary function from $H-H$.

9 pages, in Russian