Free boundary minimal surfaces in the unit three-ball via desingularization of the critical catenoid and the equatorial disc
By N. Kapouleas, M. Li. 2017
56 citations recorded by the source corpus.
Abstract 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 disc. 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 by using the min-max method.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/241159b4dbe85b71aa8847be7a2a1820aa143429
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In Applied Mathematics
- M. Li
- Marco A. M. Guaraco
- Hung Tran
- Xin Zhou
- Antoine Song
- Peter J. McGrath
- Jusuf Ramic
- Camillo De Lellis
Citations in the corpus
- Free boundary minimal surfaces in the unit ball : recent advances and open questions (2019, background): “xcellent surveys [50] [51] by Kapouleas on the basic methodology of these ideas. The rst desingularization construction of free boundary minimal surfaces in B3 was done by Kapouleas and the author in [54]. This is a highly symmetric construction with O(2)-symmetry. The idea is to take an equatorial ”