An orthorhombic deformation family of Schwarz’ H surfaces

Chen, Hao; Weber, Matthias

doi:10.1090/tran/8275

An orthorhombic deformation family of Schwarz’ H surfaces
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by Hao Chen and Matthias Weber PDF

Trans. Amer. Math. Soc. 374 (2021), 2057-2078 Request permission

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.

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