On a strong multiplicity one property for the length spectra of even dimensional compact hyperbolic spaces

TL;DR

This paper proves a strong multiplicity one theorem for the length spectra of compact even-dimensional hyperbolic spaces, showing that matching lengths for all but finitely many geodesics implies complete spectral equivalence.

Contribution

It establishes a new strong multiplicity one property for length spectra in even-dimensional hyperbolic spaces, extending spectral uniqueness results.

Findings

If all but finitely many geodesic lengths match, then all lengths match.

The result applies specifically to compact even-dimensional hyperbolic spaces.

It advances understanding of spectral rigidity in hyperbolic geometry.

Abstract

We prove a strong multiplicity one theorem for the length spectrum of compact even dimensional hyperbolic spaces i.e. if all but finitely many closed geodesics for two compact even dimensional hyperbolic spaces have the same length, then all closed geodesics have the same length.