A new deformation family of Schwarz' D surface

Hao Chen; Matthias Weber

A new deformation family of Schwarz' D surface

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arxiv 1804.01442 v2 pith:5MKG25I6 submitted 2018-04-04 math.DG math.CV

Hao Chen , Matthias Weber This is my paper · ORCID

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keywords familyclassicaldeformationsdeltamanyparameterschwarzsurface

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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.

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Stacking disorder in periodic minimal surfaces
math.DG 2019-08 conditional novelty 7.0 of 10

Balanced, non-degenerate node configurations on a flat torus produce 1-parameter families of embedded, non-periodic minimal surfaces of infinite genus, with prescribed stacking disorder.

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