On ideal vertices of right-angled hyperbolic polyhedra

2023/03/16 by Stepan Alexandrov, Alexandrov, Stepan
Mathematics · #Analytic and geometric function theory #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2303.09533

openalex publication_date 2023/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we improve Nikulin's inequality in the case of right-angled hyperbolic polyhedra. The new inequality allows to give much shorter proofs of the known dimension bounds. We also improve Nonaka's lower bound on the number of ideal vertices for right-angled hyperbolic polyhedra.

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