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Rigidity theorems in the hyperbolic space

Henrique Fernandes de Lima
대한수학회 (The Korean Mathematical Society)|2013.01|대한수학회보 (Bulletin of the KMS)|제50권 제1호|pp. 97-103

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참고문헌

키워드

Gauss maphyperbolic spacemean curvaturecomplete hypersurfaces
주제분류수학

초록

As a suitable application of the well known generalized max- imum principle of Omori-Yau, we obtain rigidity results concerning to a complete hypersurface immersed with bounded mean curvature in the (n+ 1)-dimensional hyperbolic space Hn+1. In our approach, we explore the existence of a natural duality between Hn+1 and the half Hn+1 of the de Sitter space Sn+1 1 , which models the so-called steady state space.

Abstract

As a suitable application of the well known generalized max- imum principle of Omori-Yau, we obtain rigidity results concerning to a complete hypersurface immersed with bounded mean curvature in the (n+ 1)-dimensional hyperbolic space Hn+1. In our approach, we explore the existence of a natural duality between Hn+1 and the half Hn+1 of the de Sitter space Sn+1 1 , which models the so-called steady state space.

참고문헌 (13)

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