Rank one symmetric spaces and Rigidity

TL;DR

This paper demonstrates that for rank one locally symmetric manifolds, the marked length spectrum uniquely determines their geometric structure when the limit set is sufficiently large.

Contribution

It establishes a rigidity result linking the size of the limit set to the uniqueness of geometric structure via the marked length spectrum.

Findings

Marked length spectrum determines geometry for large limit sets.

Rigidity holds specifically for rank one locally symmetric manifolds.

The size of the limit set is crucial for the spectral determination.

Abstract

In this paper we show that if the limit set is not small ,marked length spectrum determines geometric structure of rank one locally symmetric manifolds.