2023/11/06 by Balacheff, Florent, Fisac, David
#53C22. Secondary: 57K20 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Primary: 53C23
paper · doi:10.48550/arxiv.2311.03182
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.