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

J. Deibsom da Silva; A. F. de Sousa

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arXiv · 1606.04899

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

J. Deibsom da Silva·A. F. de Sousa

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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.

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BibTeX RIS

J. Deibsom da Silva, A. F. de Sousa. 2016-06-15. A Maximum Principle for hypersurfaces in $\mathbb{R}^{n+1}$ with an Ideal Contact at Infinity and Bounded Mean Curvature. https://arxiv.org/abs/1606.04899

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