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. ${\bf 20}$, 325-343 2001] and De Lima and Meeks [Indiana Univ. Math. Journal ${\bf 53}$ 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.