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arXiv · 1902.07322

Weighted Alexandrov-Fenchel inequalities in hyperbolic space and a conjecture of Ge, Wang and Wu

Frederico Girão·Diego Pinheiro·Neilha M. Pinheiro·Diego Rodrigues
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Abstract

We consider a conjecture made by Ge, Wang and Wu regarding weighted Alexandrov-Fenchel inequalities for horospherically convex hypersurfaces in hyperbolic space (a bound, for some physically motivated weight function, of the weighted integral of the $k^{\mathrm{th}}$ mean curvature in terms of the area of the hypersurface). We prove an inequality very similar to the conjectured one. Moreover, when $k$ is zero and the ambient space has dimension three, we give a counterexample to the conjectured inequality.

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Frederico Girão, Diego Pinheiro, Neilha M. Pinheiro, Diego Rodrigues. 2019-02-19. Weighted Alexandrov-Fenchel inequalities in hyperbolic space and a conjecture of Ge, Wang and Wu. https://arxiv.org/abs/1902.07322

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