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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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


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:
  • Matthias Weber
  • Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
  • MR Author ID: 354770
  • ORCID: 0000-0003-2691-2203
  • Email:
  • 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.
  • © Copyright 2021 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 374 (2021), 2785-2803
  • MSC (2020): Primary 53A10
  • DOI:
  • MathSciNet review: 4223033