Isoperimetry and the properness of weak 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.

v2 update: the result is extended to all dimensions, organizational and writing improvements are made. 19 pages. Final version, to appear in Calc. Var. PDE