Title: The inverse mean curvature flow as an obstacle problem

Authors: Roger Moser

Issue: Volume 57 (2008), Issue 5, 2235-2256

Abstract: The inverse mean curvature flow is a geometric evolution problem that is turned into a degenerate elliptic problem by a level set formulation. In the latter form, it may be regarded as a special case of an obstacle problem. In this paper, solutions of the problem are constructed with an approximation by $p$-harmonic functions and the use of appropriate barrier functions. This also extends the known existence results for weak solutions of the inverse mean curvature flow.