A new deformation family of Schwarz' D surface
Abstract
We prove the existence of a new 2-parameter family o$\Delta$ of embedded triply periodic minimal surfaces of genus 3. The new surfaces share many properties with classical orthorhombic deformations of Schwarz' D surface, but also exotic in many ways. In particular, they do not belong to Meeks' five-dimensional family. Nevertheless, o$\Delta$ meets classical deformations in a 1-parameter family on its boundary.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2018
- DOI:
- 10.48550/arXiv.1804.01442
- arXiv:
- arXiv:1804.01442
- Bibcode:
- 2018arXiv180401442C
- Keywords:
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- Mathematics - Differential Geometry;
- Mathematics - Complex Variables;
- 53A10
- E-Print:
- 17 pages, 7 figures