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

2024/09/14 by Chu, Adrian Chun-Pong, Li, Yangyang · 2 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2409.09315

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.

Cited by

• Pairs of Embedded Spheres with Pinched Prescribed Mean Curvature
• Min-max theory and minimal surfaces with prescribed genus

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