On volumes of hyperbolic right-angled polyhedra

Stepan Alexandrov; Nikolay Bogachev; Andrei Egorov; Andrei Vesnin

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arXiv · 2111.08789

On volumes of hyperbolic right-angled polyhedra

Stepan Alexandrov·Nikolay Bogachev·Andrei Egorov·Andrei Vesnin

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Abstract

In this paper we obtain new upper bounds on volumes of right-angled polyhedra in hyperbolic space $\mathbb{H}^3$ in three different cases: for ideal polyhedra with all vertices on the ideal hyperbolic boundary, for compact polytopes with only finite (or usual) vertices, and for finite volume polyhedra with vertices of both types.

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BibTeX RIS

Stepan Alexandrov, Nikolay Bogachev, Andrei Egorov, Andrei Vesnin. 2022-01-04. On volumes of hyperbolic right-angled polyhedra. https://arxiv.org/abs/2111.08789

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