Embedded minimal tori in \(S^3\) and the Lawson conjecture
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Publication:392787
DOI10.1007/s11511-013-0101-2zbMath1305.53061arXiv1203.6597OpenAlexW2070969849WikidataQ56170034 ScholiaQ56170034MaRDI QIDQ392787
Publication date: 15 January 2014
Published in: Acta Mathematica (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1203.6597
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Noncollapsing in mean-convex mean curvature flow
- Subsequent singularities in mean-convex mean curvature flow
- A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order
- A first eigenvalue estimate for minimal hypersurfaces
- Minimal immersions of surfaces by the first eigenfunctions and conformal area
- New minimal surfaces in S 3
- Shortening embedded curves
- A distance comparison principle for evolving curves
- Min-max theory and the Willmore conjecture
- Some interior regularity theorems for minimal surfaces and an extension of Bernstein's theorem
- Local rigidity theorems for minimal hypersurfaces
- Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérées
- Minimal varieties in Riemannian manifolds
- Complete minimal surfaces in \(S^ 3\)
- The unknottedness of minimal embeddings
- Minimal submanifolds of low cohomogeneity
- Minimal Surfaces with Low Index in the Three-Dimensional Sphere
- Minimal surfaces in the three-sphere by doubling the Clifford torus
- First eigenvalue of symmetric minimal surfaces in $\mathbb{S}^3$
- Doubling and Desingularization Constructions for Minimal Surfaces
- The nature of singularities in mean curvature flow of mean-convex sets
- A two-piece property for compact minimal surfaces in a three-sphere
- The size of the singular set in mean curvature flow of mean-convex sets