The weak convergence of varifolds generated by rectifiable flat G-chains

TL;DR

This paper proves that under certain conditions, the convergence of rectifiable chains in flat norm guarantees the weak convergence of associated rectifiable varifolds, linking geometric measure theory concepts.

Contribution

It establishes a new link between flat chain convergence and varifold convergence, expanding understanding in geometric measure theory.

Findings

Flat chain convergence implies varifold weak convergence under mass convergence.

The result applies when the limit flat chain is rectifiable.

Provides conditions for convergence in geometric measure theory.

Abstract

In the present paper, we prove that the convergence of rectifiable chains in flat norm implies the weak convergence of associated rectifiable varifolds if the limit flat chain is rectifiable and the mass converges also to the mass of limit chain.