A Uniqueness Result for Self-expanders with Small Entropy

TL;DR

This paper proves a uniqueness result for small entropy self-expanders asymptotic to a fixed cone, using the mountain-pass theorem and integer degree argument, contributing to the understanding of geometric flows.

Contribution

It introduces a new uniqueness theorem for small entropy self-expanders based on advanced variational and topological methods.

Findings

Uniqueness of small entropy self-expanders asymptotic to a fixed cone

Application of mountain-pass theorem in geometric analysis

Use of integer degree argument for proving uniqueness

Abstract

In this short note, we prove a uniqueness result for small entropy self-expanders asymptotic to a fixed cone. This is a direct consequence of the mountain-pass theorem and the integer degree argument proved by J. Bernstein and L. Wang.