Abstract
AbstractWe consider the evolution of hypersurfaces with boundary under inverse mean curvature flow. The boundary condition is of Neumann type, i.e. the evolving hypersurface moves along, but stays perpendicular to, a fixed supporting hypersurface. In this setup, we prove existence and uniqueness of weak solutions. Furthermore, we indicate the existence of a monotone quantity which is the analog of the Hawking mass for closed hypersurfaces.
Funder
Max Planck Institute for Gravitational Physics in Potsdam
Swiss National Science Foundation SNF
Subject
Applied Mathematics,General Mathematics
Reference70 articles.
1. Optimal Hölder regularity for mixed boundary value problems;J. Math. Anal. Appl.,1989
2. Subsolutions to the least area problem and the minimal hull of a bounded set in ℝn{\mathbb{R}^{n}};Ann. Univ. Ferrara Sez. VII Sci. Mat.,1984
3. Proof of the Riemannian Penrose inequality using the positive mass theorem;J. Differential Geom.,2001
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