Subgraphs of BV functions on RCD spaces

IF 0.6 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2024-02-17 DOI:10.1007/s10455-024-09945-0

引用次数: 0

Abstract

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 \({\textsf{X}}\times \mathbb R\) , where \({\textsf{X}}\) is an \({\textrm{RCD}}(K,N)\) metric measure space. In particular, we give the precise expression of the push-forward onto \({\textsf{X}}\) of the perimeter measure of the subgraph in \({\textsf{X}}\times \mathbb R\) of a \({\textrm{BV}}\) function on \({\textsf{X}}\) . Moreover, in properly chosen good coordinates, we write the precise expression of the normal to the boundary of the subgraph of a \({\textrm{BV}}\) function f with respect to the polar vector of f, and we prove change-of-variable formulas.

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RCD 空间上的 BV 函数子图

摘要在这项工作中，我们将在\(\mathbb R^n\times \mathbb R\) 中的有界变化函数子图的经典结果扩展到了\({\textsf{X}}\times \mathbb R\) 中，其中\({\textsf{X}}\) 是一个 \({\textrm{RCD}}(K,N)\) 度量空间。特别地，我们给出了一个函数在\({\textsf{X}}\)上的\({\textrm{BV}}\)子图的周长度量的前推到\({\textsf{X}}\)的精确表达式。此外，在正确选择的良好坐标中，我们写出了关于 f 的极向量的 \({\textrm{BV}} 函数 f 子图边界法线的精确表达式，并证明了变量变化公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.