Work

A Basmajian-type inequality for Riemannian surfaces

Year: 2025

Type: article

Abstract: We explore compact Riemannian surfaces whose boundary consists of a single closed geodesic and the relationship between orthospectrum and boundary length. More precisely, we establish a uniform lower bound on the boundary length in terms of the orthospectrum when fixing a metric invariant of the surface related to the classical notion of volume entropy. This inequality can be thought of as a Riemannian analog of Basmajian’s identity for hyperbolic surfaces.

Source: Journal of Topology and Analysis

DOI: 10.1142/s1793525325500104

Authors: Florent Balacheff, David Fisac

Institutions: Universitat Autònoma de Barcelona, Centre de Recerca Matemàtica

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Fonds National de la Recherche Luxembourg, Ministerio de Ciencia e Innovación, Agència de Gestió d'Ajuts Universitaris i de Recerca, Agencia Estatal de Investigación