Subgraphs of BV functions on RCD spaces

Abstract

In this work we extend classical results for subgraphs of functions of bounded variation in Rn×R to the setting of X×R, where X is an RCD(K,N) metric measure space. In particular, we give the precise expression of the push-forward onto X of the perimeter measure of the subgraph in X×R of a BV function on X. Moreover, in properly chosen good coordinates, we write the precise expression of the normal to the boundary of the subgraph of a BV function f with respect to the polar vector of f, and we prove change-of-variable formulas.