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

Girão, Frederico; Pinheiro, Diego; Pinheiro, Neilha; Rodrigues, Diego

doi:10.1090/proc/15127

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

Authors: Frederico Girão, Diego Pinheiro, Neilha M. Pinheiro and Diego Rodrigues
Journal: Proc. Amer. Math. Soc. 149 (2021), 369-382
MSC (2020): Primary 51M16; Secondary 53E10, 53A35
DOI: https://doi.org/10.1090/proc/15127
Published electronically: October 16, 2020
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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 th mean curvature in terms of the area of the hypersurface). We prove an inequality very similar to the conjectured one. Moreover, when is zero and the ambient space has dimension three, we give a counterexample to the conjectured inequality.

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