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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A new deformation family of Schwarz’ D surface


Authors: Hao Chen and Matthias Weber
Journal: Trans. Amer. Math. Soc. 374 (2021), 2785-2803
MSC (2020): Primary 53A10
DOI: https://doi.org/10.1090/tran/8274
Published electronically: January 12, 2021
MathSciNet review: 4223033
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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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Additional Information

Hao Chen
Affiliation: Georg-August-Universität Göttingen, Institut für Numerische und Angewandte Mathematik, Lotzestr. 16-18, D-37083 Göttingen, Germany
ORCID: 0000-0003-1087-2868
Email: h.chen@math.uni-goettingen.de

Matthias Weber
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
MR Author ID: 354770
ORCID: 0000-0003-2691-2203
Email: matweber@indiana.edu

Keywords: Triply periodic minimal surfaces
Received by editor(s): August 28, 2018
Received by editor(s) in revised form: July 27, 2020
Published electronically: January 12, 2021
Additional Notes: The first author was supported by Individual Research Grant from Deutsche Forschungsgemeinschaft within the project “Defects in Triply Periodic Minimal Surfaces”, Projektnummer 398759432.
Article copyright: © Copyright 2021 American Mathematical Society