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Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature

William Meeks III Leon Simon Shing-Tung Yau

Differential Geometry mathscidoc:1912.43475

Annals of Mathematics, 621-659, 1982.11
Let N be a three dimensional Riemannian manifold. Let E be a closed embedded surface in N. Then it is a question of basic interest to see whether one can deform: in its isotopy class to some" canonical" embedded surface. From the point of view of geometry, a natural" canonical" surface will be the extremal surface of some functional defined on the space of embedded surfaces. The simplest functional is the area functional. The extremal surface of the area functional is called the minimal surface. Such minimal surfaces were used extensively by Meeks-Yau [MY21 in studying group actions on three dimensional manifolds.
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@inproceedings{william1982embedded,
  title={Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature},
  author={William Meeks III, Leon Simon, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203505906162039},
  booktitle={Annals of Mathematics},
  pages={621-659},
  year={1982},
}
William Meeks III, Leon Simon, and Shing-Tung Yau. Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature. 1982. In Annals of Mathematics. pp.621-659. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203505906162039.
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