The Smale conjecture and min-max theory

TL;DR

This paper presents a novel proof of the Smale conjecture for real projective 3-space and lens spaces by employing minimal surface techniques and min-max theory, offering an alternative to Ricci flow methods.

Contribution

The authors provide a new proof of the Smale conjecture for $ ext{RP}^3$ and lens spaces using minimal surface and min-max theory, expanding the toolkit beyond Ricci flow approaches.

Findings

Proof of the Smale conjecture for $ ext{RP}^3$ and lens spaces.

Application of minimal surface and min-max theory to topological conjectures.

Alternative proof method to Ricci flow for the Smale conjecture.

Abstract

We give a new proof of the Smale conjecture for $\mathbb{RP}^3$ and all lens spaces using minimal surfaces and min-max theory. For $\mathbb{RP}^3$, the conjecture was first proved in 2019 by Bamler-Kleiner using Ricci flow.