Isoperimetry and the properness of weak inverse mean curvature flow

TL;DR

This paper establishes a new existence theorem for proper solutions to the weak inverse mean curvature flow, relying on isoperimetric profile conditions without requiring curvature assumptions.

Contribution

It introduces a novel existence result for weak inverse mean curvature flow under isoperimetric profile conditions, expanding applicability without curvature constraints.

Findings

Proves existence of proper solutions under non-degeneracy conditions.

No curvature assumptions are needed for the existence theorem.

Connects isoperimetric profile properties with inverse mean curvature flow.

Abstract

We prove a new existence theorem for proper solutions of Huisken and Ilmanen's weak inverse mean curvature flow, assuming certain non-degeneracy conditions on the isoperimetric profile. In particular, no curvature assumption is imposed in our existence theorem.