Hessian measures in the class of m-convex (m 􀀀 cv) functions

Abstract

The theory of m-convex (m􀀀 cv) functions is a new direction in the real geometry. In this work, by using the connection m 􀀀 cv functions with strongly m-subharmonic (shm) functions and using well-known and rich properties of shm functions, we show a number of important properties of the class of m􀀀cv functions, in particular, we study Hessians Hk(u); k = 1; 2; :::; n 􀀀 m + 1; in the class of bounded m 􀀀 cv functions.