A sharp estimate for the genus of embedded surfaces in the 3-sphere

DOI10.1007/S12220-024-01689-4zbMATH Open1548.53066MaRDI QIDQ6564130

Kwok-Kun Kwong

Publication date: 28 June 2024

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

zbMATH Keywords

minimal surfaces\(3\)-manifoldscompactness theoremsgenus estimates

Mathematics Subject Classification ID

Global submanifolds (53C40) Rigidity results (53C24) General topology of 3-manifolds (57K30)

Cites Work

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• Embedded minimal tori in \(S^3\) and the Lawson conjecture
• Optimal rigidity estimates for nearly umbilical surfaces
• A first eigenvalue estimate for minimal hypersurfaces
• The space of minimal embeddings of a surface into a three-dimensional manifold of positive Ricci curvature
• Ricci curvature, geodesics and some geometric properties of Riemannian manifolds with boundary
• A \(C^{0}\) estimate for nearly umbilical surfaces
• Minimal varieties in Riemannian manifolds
• Complete minimal surfaces in \(S^ 3\)
• A general comparison theorem with applications to volume estimates for submanifolds
• Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length

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