A compactness result for BV functions in metric spaces

TL;DR

This paper establishes a compactness theorem for BV functions in metric spaces with varying metrics, and demonstrates its application to Carnot-Carathéodory spaces, advancing the understanding of BV functions in non-Euclidean settings.

Contribution

It introduces a new compactness result for BV functions in metric spaces with changing metrics, extending classical results to more general spaces.

Findings

Proves a compactness theorem for BV functions in variable metric spaces.

Applies the result to Carnot-Carathéodory spaces.

Enhances understanding of BV functions in non-Euclidean geometries.

Abstract

We prove a compactness result for bounded sequences $(u_j)_j$ of functions with bounded variation in metric spaces $(X,d_j)$ where the space $X$ is fixed but the metric may vary with $j$. We also provide an application to Carnot-Carath\'eodory spaces.