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arXiv · 2311.03182

A Basmajian-type inequality for Riemannian surfaces

Florent Balacheff·David Fisac
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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.

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Florent Balacheff, David Fisac. 2025-03-03. A Basmajian-type inequality for Riemannian surfaces. https://arxiv.org/abs/2311.03182

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