A new deformation family of Schwarz’ D surface

Chen, Hao; Weber, Matthias

doi:10.1090/tran/8274

A new deformation family of Schwarz’ D surface
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by Hao Chen and Matthias Weber PDF

Trans. Amer. Math. Soc. 374 (2021), 2785-2803 Request permission

Abstract:

We prove the existence of a new 2-parameter family $\mathrm {o\Delta }$ 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’ 5-dimensional family. Nevertheless, $\mathrm {o\Delta }$ meets classical deformations in a 1-parameter family on its boundary.

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