On volumes of hyperbolic right-angled polyhedra

TL;DR

This paper establishes new upper bounds on the volumes of hyperbolic right-angled polyhedra across various vertex configurations, enhancing understanding of their geometric properties in hyperbolic space.

Contribution

It provides novel upper bounds for volumes of hyperbolic right-angled polyhedra in three vertex scenarios, expanding previous geometric volume estimates.

Findings

New upper bounds for ideal polyhedra volumes

Upper bounds for compact polyhedra volumes

Volume estimates for mixed-vertex polyhedra

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.