Subgraphs of BV functions on RCD spaces

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