Hessian measures in the class of $m$-convex functions

In this talk we show a number of important properties of the class of $m-cv$ functions, in particular, we study Hessians ${{H}^{k}}(u)$, $k=1,2,\ldots,n-m+1$, in the class of bounded $m-cv$ functions by using the connection of $m-cv$ functions with $m$-subharmonic $s{{h}_{m}}$ functions and using well-known and rich properties of $s{{h}_{m}}$ functions.