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Boundary length and spectrum

Published on:

6 November 2023

Primary Category:

Differential Geometry

Paper Authors:

Florent Balacheff,

David Fisac


Key Details

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

AI generated summary

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.

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