# Generic uniqueness of expanders with vanishing relative entropy

## TL;DR

This paper introduces a relative entropy concept for mean curvature flow expanders and proves that, under generic conditions, such expanders with zero relative entropy are unique, highlighting a new uniqueness result in geometric analysis.

## Contribution

It establishes the generic uniqueness of expanders with vanishing relative entropy for mean curvature flow, extending previous work and using recent advances in the field.

## Key findings

- Expanders with zero relative entropy are generically unique.
- Locally entropy minimizing expanders are also generically unique.
- The work adapts and extends White's and Bernstein's results in geometric analysis.

## Abstract

We define a relative entropy for two expanding solutions to mean curvature flow of hypersurfaces, asymptotic to the same cone at infinity. Adapting work of White and using recent results of Bernstein and Bernstein-Wang, we show that expanders with vanishing relative entropy are unique in a generic sense. This also implies that generically locally entropy minimising expanders are unique.