A Maximum Principle for hypersurfaces in ${\mathbb{R}}^{n+1}$ with an Ideal Contact at Infinity and Bounded Mean Curvature

Abstract

We will generalize a Maximum Principle at Infinity in the parabolic case given by De Lima [Ann. Global Anal. Geom. $20$, 325-343 2001] and De Lima and Meeks [Indiana Univ. Math. Journal $53$ 5, 1211-1223 2004], for disjoints hypersurfaces of ${\mathbb{R}}^{n+1}$ with bounded mean curvature without restrictions on the Gaussian curvature. We will also extend for hypersurfaces in ${\mathbb{R}}^{n+1}$ a generalization of Hopf's Maximum Principle for hypersurfaces that get close asymptotically.

arXiv comment20 pages, 1 figure

References in corpus (1)

• Global maximum principles and divergence theorems on complete manifolds with boundary