An orthorhombic deformation family of Schwarz' H surfaces
Abstract
The classical H surfaces of H. A. Schwarz form a 1-parameter family of triply periodic minimal surfaces (TPMS) that are usually described as close relatives to his more famous P surface. However, a crucial distinction between these surfaces is that the P surface belongs to a 5-dimensional smooth family of embedded TPMS of genus three discovered by W. Meeks, while the H surfaces are among the few known examples outside this family. We construct a 2-parameter family of embedded TPMS of genus three that contains the H family and meets the Meeks family. In particular, we prove that H surfaces can be deformed continuously within the space of TPMS of genus three into Meeks surfaces.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2018
- DOI:
- 10.48550/arXiv.1807.10631
- arXiv:
- arXiv:1807.10631
- Bibcode:
- 2018arXiv180710631C
- Keywords:
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- Mathematics - Differential Geometry;
- Mathematics - Complex Variables;
- 53A10
- E-Print:
- 20 pages, 11 figures. arXiv admin note: text overlap with arXiv:1804.01442