On a generalized 1-harmonic equation and the inverse mean curvature flow
Journal
Journal of Geometry and Physics
Journal Volume
61
Journal Issue
2
Pages
453-461
Date Issued
2011
Author(s)
Abstract
We introduce and study generalized 1-harmonic equations (1.1). Using some ideas and techniques in studying 1-harmonic functions from Wei (2007) [1], and in studying nonhomogeneous 1-harmonic functions on a cocompact set from Wei (2008) [2, (9.1)], we find an analytic quantity w in the generalized 1-harmonic equations (1.1) on a domain in a Riemannian n-manifold that affects the behavior of weak solutions of (1.1), and establish its link with the geometry of the domain. We obtain, as applications, some gradient bounds and nonexistence results for the inverse mean curvature flow, Liouville theorems for p-subharmonic functions of constant p-tension field, p>n, and nonexistence results for solutions of the initial value problem of inverse mean curvature flow. © 2010 Elsevier B.V.
Type
journal article