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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A global pinching theorem for compact minimal surfaces in $ S\sp 3$


Author: Yi-Jung Hsu
Journal: Proc. Amer. Math. Soc. 113 (1991), 1041-1044
MSC: Primary 53C42; Secondary 53C20
DOI: https://doi.org/10.1090/S0002-9939-1991-1086331-8
MathSciNet review: 1086331
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Abstract: Let $ M$ be a compact minimally immersed surface in the unit sphere $ {S^3}$, and let $ S$ denote the square of the length of the second fundamental form of $ M$. We prove that if $ {\left\Vert S \right\Vert _2} \leq 2\sqrt 2 \pi $, then $ M$ is either the equatorial sphere or the Clifford torus.


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DOI: https://doi.org/10.1090/S0002-9939-1991-1086331-8
Article copyright: © Copyright 1991 American Mathematical Society