论文标题
$ \ rm bv $ functions $ \ rm rm rcd $ spaces的子图
Subgraphs of $\rm BV$ functions on $\rm RCD$ spaces
论文作者
论文摘要
在这项工作中，我们将$ \ Mathbb {r}^n \ times \ Mathbb {r} $中有限变化功能的子图的经典结果扩展到$ \ Mathsf {x} \ times \ times \ times \ times \ times \ mathbb {r} $，其中$ \ mathsf {x Mathsf {x MATHSF {x MOTUIT $ nes $ metrrir a a $ rm rm rm rm rm rm rm rm rm rm rm rm rm rm rm rm rm c In particular, we give the precise expression of the push-forward onto $\mathsf{X}$ of the perimeter measure of the subgraph in $\mathsf{X}\times\mathbb{R}$ of a $\rm BV$ function on $\mathsf{X}$.此外，在正确选择的良好坐标中，我们将正常的精确表达式与$ f $的极性向量相对于$ \ rm bv $函数$ f $的子图的边界，我们证明了可变量的公式。
In this work we extend classical results for subgraphs of functions of bounded variation in $\mathbb{R}^n\times\mathbb{R}$ to the setting of $\mathsf{X}\times\mathbb{R}$, where $\mathsf{X}$ is an ${\rm RCD}(K,N)$ metric measure space. In particular, we give the precise expression of the push-forward onto $\mathsf{X}$ of the perimeter measure of the subgraph in $\mathsf{X}\times\mathbb{R}$ of a $\rm BV$ function on $\mathsf{X}$. Moreover, in properly chosen good coordinates, we write the precise expression of the normal to the boundary of the subgraph of a $\rm BV$ function $f$ with respect to the polar vector of $f$, and we prove change-of-variable formulas.
