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Blaine Lawson:三维球面中的紧致极小曲面——Joseph Fels Ritt Lectures 1
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https://www.youtube.com/watch?v=iLTzhG1WadQ Columbia University Department of Mathematics Spring 2024 Joseph Fels Ritt Lectures (Blaine Lawson) 02-15-2024 Blaine Lawson——”On compact minimal surfaces in S^3“:https://www.math.columbia.edu/~staff/lawson1-new.pdf Simon Brendle——“Embedded minimal tori in S^3 and the Lawson conjecture”:https://doi.org/10.1007/s11511-013-0101-2 Wu-yi Hsiang, H. Blaine Lawson, Jr.——“Minimal submanifolds of low cohomogeneity”:https://doi.org/10.4310/jdg/1214429775 H. Blaine Lawson, Jr.——“Local Rigidity Theorems for Minimal Hypersurfaces”:https://doi.org/10.2307/1970816 H. Blaine Lawson, Jr.——“Complete Minimal Surfaces in S^3”:https://doi.org/10.2307/1970625 H. Blaine Lawson, Jr.——“The unknottedness of minimal embeddings”:https://doi.org/10.1007/BF01404649 Simon Brendle——“Minimal surfaces in S^3: a survey of recent results”:https://doi.org/10.1007/s13373-013-0034-2 In this survey, we discuss various aspects of the minimal surface equation in the three-sphere S^3. After recalling the basic definitions, we describe a family of immersed minimal tori with rotational symmetry. We then review the known examples of embedded minimal surfaces in S^3. Besides the equator and the Clifford torus, these include the Lawson and Kapouleas-Yang examples, as well as a new family of examples found recently by Choe and Soret. We next discuss uniqueness theorems for minimal surfaces in S^3, such as the work of Almgren on the genus 0 case, and our recent solution of Lawson's conjecture for embedded minimal surfaces of genus 1. More generally, we show that any minimal surface of genus 1 which is Alexandrov immersed must be rotationally symmetric. We also discuss Urbano's estimate for the Morse index of an embedded minimal surface and give an outline of the recent proof of the Willmore conjecture by Marques and Neves. Finally, we describe estimates for the first eigenvalue of the Laplacian on a minimal surface.
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