A Basmajian-type inequality for Riemannian surfaces
Differential Geometry
2025-03-04 v3 Geometric Topology
Abstract
We explore for compact Riemannian surfaces whose boundary consists of a single closed geodesic 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.
Keywords
Cite
@article{arxiv.2311.03182,
title = {A Basmajian-type inequality for Riemannian surfaces},
author = {Florent Balacheff and David Fisac},
journal= {arXiv preprint arXiv:2311.03182},
year = {2025}
}
Comments
Accepted version to be published in Journal of Topology Analysis