An isoperimetric inequality for diffused surfaces

TL;DR

This paper establishes an isoperimetric inequality for varifolds in Euclidean space, extending the theory of weakly differentiable functions and deriving Sobolev inequalities to aid in the analysis of diffused surfaces.

Contribution

It introduces an isoperimetric inequality for varifolds and adapts weakly differentiable function theory to support diffused surface studies.

Findings

Proves an isoperimetric inequality for general varifolds.

Develops Sobolev type inequalities for varifold functions.

Facilitates the application of varifold theory to diffused surfaces.

Abstract

For general varifolds in Euclidean space, we prove an isoperimetric inequality, adapt the basic theory of generalised weakly differentiable functions, and obtain several Sobolev type inequalities. We thereby intend to facilitate the use of varifold theory in the study of diffused surfaces.