Fractional Sobolev norms and BV functions on manifolds

Abstract

The bounded variation seminorm and the Sobolev seminorm on compact manifolds are represented as a limit of fractional Sobolev seminorms. This establishes a characterization of functions of bounded variation and of Sobolev functions on compact manifolds. As an application the special case of sets of finite perimeter is considered.

changes from previous version: case p > 1 included, Lemma 2.2 added for clarification, typos corrected