Published on:

6 November 2023

Primary Category:

Differential Geometry

Paper Authors:

Florent Balacheff,

David Fisac

•

Proves lower bound on boundary length using spectrum and volume entropy

•

Generalizes Basmajian's identity to any Riemannian surface

•

Uses metric graphs to prove result before transferring to surfaces

•

Provides examples of sharpness and non-sharpness of bound

•

Volume entropy controls growth rate of metric balls in universal cover

Boundary length and spectrum

This paper explores the relationship between the length of the boundary and the spectrum of a compact Riemannian surface. It proves a lower bound on the boundary length in terms of the spectrum when the volume entropy is fixed. This can be seen as a generalization of Basmajian's identity to surfaces without curvature constraints.

Length spectrum of random hyperbolic 3-manifolds

Minimal hypersurfaces in the sphere have improved eigenvalue bounds

A more interpretable title summarizing the key contributions

Precompactness of domains under Ricci curvature bound

Spectral gaps on negatively curved surfaces

Proof of lower bound on periodicity for spectrum classifying 2D quantum field theories

No comments yet, be the first to start the conversation...

Sign up to comment on this paper