# Almost maximal volume entropy

## TL;DR

This paper demonstrates the existence of manifolds that nearly achieve maximal volume entropy without being hyperbolic, challenging assumptions about the relationship between entropy and hyperbolic geometry.

## Contribution

It establishes the existence of non-hyperbolic manifolds with almost maximal volume entropy, expanding understanding of geometric entropy properties.

## Key findings

- Existence of manifolds with almost maximal volume entropy
- Such manifolds are not hyperbolic
- Challenges previous assumptions about entropy and hyperbolicity

## Abstract

We prove the existence of manifolds with almost maximal volume entropy which are not hyperbolic.