Existence of 5 minimal tori in 3-spheres of positive Ricci curvature

TL;DR

This paper proves that every 3-sphere with positive Ricci curvature contains at least five embedded minimal tori, confirming a longstanding conjecture using min-max theory inspired by mean curvature flow.

Contribution

It establishes the existence of at least five minimal tori in positively Ricci curved 3-spheres, confirming White's conjecture.

Findings

Confirmed White's conjecture for positive Ricci curvature

Established at least five embedded minimal tori in such 3-spheres

Used min-max theory inspired by mean curvature flow

Abstract

In 1989, B. White conjectured that every Riemannian 3-sphere has at least 5 embedded minimal tori. We confirm this conjecture for 3-spheres of positive Ricci curvature. While our proof uses min-max theory, the underlying heuristics are largely inspired by mean curvature flow.