Embedded minimal tori in S³ and the Lawson conjecture

2012/03/29 by Simon Brendle, Brendle, S. · 7 citations
Mathematics · #Geometric and Algebraic Topology #Geometry and complex manifolds #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1203.6597

Abstract

We show that any embedded minimal torus in S³ is congruent to the Clifford torus. This answers a question posed by H.B. Lawson, Jr., in 1970.

Citations

• Local Rigidity Theorems for Minimal Hypersurfaces
• The unknottedness of minimal embeddings

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• Minimally embedded Riemann surfaces in \mbS³ and the conformal deformation of their metrics
• Noncollapsing for Curvature Flows with Inhomogeneous Speeds
• The First Eigenvalue of Embedded Minimal Hypersurfaces in the Unit Sphere I: Yau's Conjecture
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