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Title of Journal: Calc Var

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Abbravation: Calculus of Variations and Partial Differential Equations

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Springer Berlin Heidelberg

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DOI

10.1002/chin.200139024

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1432-0835

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A Penrose inequality for graphs over Kottler space

Authors: Yuxin Ge Guofang Wang Jie Wu Chao Xia
Publish Date: 2014/05/03
Volume: 52, Issue: 3-4, Pages: 755-782
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Abstract

In this work we prove an optimal Penrose inequality for asymptotically locally hyperbolic manifolds which can be realized as graphs over Kottler space Such inequality relies heavily on an optimal weighted Alexandrov–Fenchel inequality for the mean convex starshaped hypersurfaces in Kottler spaceG Wang and J Wu are partly supported by SFB/TR71 “Geometric partial differential equations” of DFG Part of this work was done while CX was visiting the mathematical institute of AlbertLudwigsUniversität Freiburg He would like to thank the institute for its hospitalityWith the same method one can represent all rotationally symmetric graphs with horizon over P kappa m in Q kappa m as rotationally symmetric graphs over P kappa m in Q kappa m for m m We believe that this statement is also true for nonrotationally symmetric graphs ie all graphs over P kappa m in Q kappa m can be represented as graphs over P kappa m in Q kappa m for m mIn the next example we show that for any mm c there are ALH graphs over P kappa m in Q kappa m m cle m m with a horizon and the dominant condition R+nn1ge 0 which can not be represented as ALH graphs in Q kappa m and can also not be represented as ALH graphs in Q kappa m for mm

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