Equivariant min-max theory
Abstract
We develop an equivariant min-max theory as proposed by Pitts-Rubinstein in 1988 and then show that it can produce many of the known minimal surfaces in $\mathbb{S}^3$ up to genus and symmetry group. We also produce several new infinite families of minimal surfaces in $\mathbb{S}^3$ proposed by Pitts-Rubinstein. These examples are doublings and desingularizations of stationary integral varifolds in $\mathbb{S}^3$.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2016
- DOI:
- 10.48550/arXiv.1612.08692
- arXiv:
- arXiv:1612.08692
- Bibcode:
- 2016arXiv161208692K
- Keywords:
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- Mathematics - Differential Geometry;
- Mathematics - Analysis of PDEs