On volumes of hyperbolic right-angled polyhedra

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Abstract

New upper bounds for the volumes of right-angled polyhedra in hyperbolic space $\mathbb{H}^3$ are obtained in the following three cases: for ideal polyhedra with all vertices on the ideal hyperbolic boundary; for compact polyhedra with only finite vertices; and for finite-volume polyhedra with vertices of both types.Bibliography: 23 titles.

About the authors

Stepan Andreevich Alexandrov

Moscow Institute of Physics and Technology (National Research University)

without scientific degree, no status

Nikolay Vladimirovich Bogachev

Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute); Moscow Institute of Physics and Technology (National Research University)

without scientific degree, no status

Andrei Yurievich Vesnin

Tomsk State University; Novosibirsk State University; Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Email: vesnin@math.nsc.ru
Doctor of physico-mathematical sciences, Senior Researcher

Andrei Aleksandrovich Egorov

Novosibirsk State University

Email: a.egorov2@g.nsu.ru

References

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Copyright (c) 2023 Alexandrov S.A., Bogachev N.V., Vesnin A.Y., Egorov A.A.

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