Existence of the tetragonal and rhombohedral deformation families of the gyroid

DOI10.1512/iumj.2021.70.8505zbMath1479.53011arXiv1901.04006OpenAlexW2913693471MaRDI QIDQ3380490

Hao Chen

Publication date: 29 September 2021

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.04006

zbMATH Keywords

Weierstrass datatriply periodic minimal surfacesgyroid4-fold saddle towersLidinoid

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10)

Related Items (1)

Gluing Karcher-Scherk saddle towers. I: Triply periodic minimal surfaces

Uses Software

• DLMF

Cites Work

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• A remark on limits of triply periodic minimal surfaces of genus 3
• Deformations of the gyroid and lidinoid minimal surfaces
• Triply periodic minimal surfaces bounded by vertical symmetry planes
• The triply periodic minimal surfaces of Alan Schoen and their constant mean curvature companions
• Minimal surfaces of least total curvature and moduli spaces of plane polygonal arcs
• Elliptic functions and applications
• The gyroid is embedded and has constant mean curvature companions
• Teichmüller theory and handle addition for minimal surfaces
• Global properties of minimal surfaces in \(E^ 3\) and \(E^ n\)
• On embedded complete minimal surfaces of genus zero
• On bifurcation and local rigidity of triply periodic minimal surfaces in $\protect \mathbb{R}^3$
• An orthorhombic deformation family of Schwarz’ H surfaces
• A new deformation family of Schwarz’ D surface

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