Marked length pattern rigidity for arithmetic manifolds

TL;DR

This paper proves a cocycle version of marked length spectrum rigidity, leading to new rigidity results for arithmetic hyperbolic manifolds and strengthened results for surfaces and locally symmetric manifolds.

Contribution

It introduces a cocycle approach to marked length spectrum rigidity and applies it to arithmetic hyperbolic and locally symmetric manifolds, enhancing existing rigidity results.

Findings

Marked length pattern rigidity for arithmetic hyperbolic manifolds

Strengthened length spectrum rigidity for surfaces

Cocycle version of rigidity theorem

Abstract

In this paper, we prove a cocycle version of marked length spectrum rigidity. There are two consequences. The first is marked length pattern rigidity for arithmetic hyperbolic locally symmetric manifolds. The second is strengthen marked length spectrum rigidity for surfaces and closed locally symmetric manifolds.