Free boundary minimal surfaces in the unit three-ball via desingularization of the critical catenoid and the equatorial disk

Nikolaos Kapouleas Brown University Martin Man-chun Li Chinese University of Hong Kong

Differential Geometry Geometric Analysis and Geometric Topology mathscidoc:1910.43015

arXiv preprint arXiv:1709.08556, 2017.9
We construct a new family of high genus examples of free boundary minimal surfaces in the Euclidean unit 3-ball by desingularizing the intersection of a coaxial pair of a critical catenoid and an equatorial disk. The surfaces are constructed by singular perturbation methods and have three boundary components. They are the free boundary analogue of the Costa-Hoffman-Meeks surfaces and the surfaces constructed by Kapouleas by desingularizing coaxial catenoids and planes. It is plausible that the minimal surfaces we constructed here are the same as the ones obtained recently by Ketover using the min-max method.
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@inproceedings{nikolaos2017free,
  title={Free boundary minimal surfaces in the unit three-ball via desingularization of the critical catenoid and the equatorial disk},
  author={Nikolaos Kapouleas, and Martin Man-chun Li},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020105725882969544},
  booktitle={arXiv preprint arXiv:1709.08556},
  year={2017},
}
Nikolaos Kapouleas, and Martin Man-chun Li. Free boundary minimal surfaces in the unit three-ball via desingularization of the critical catenoid and the equatorial disk. 2017. In arXiv preprint arXiv:1709.08556. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020105725882969544.
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