A Basmajian-type inequality for Riemannian surfaces

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.