# Entropies for negatively curved manifolds

## TL;DR

This paper surveys various entropy concepts associated with negatively curved compact manifolds, exploring their interrelations and the related rigidity problems in differential geometry.

## Contribution

It provides a comprehensive overview of entropy notions and their connections, highlighting recent developments and open problems in the field.

## Key findings

- Different entropy notions are interconnected in negatively curved manifolds
- Entropy plays a key role in understanding geometric rigidity
- The survey identifies open problems in entropy and rigidity theory

## Abstract

We survey several notions of entropy related to a compact manifold of negative curvature, some relations between them, and the rigidity problems.