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Shoda, Toshihiro

A reducibility for a triply periodic minimal surface. (English) Zbl 1453.53010

Shoda, Toshihiro (ed.) et al., Differential geometry and Tanaka theory. Differential system and hypersurface theory. Proceedings of the international conference, RIMS, Kyoto University, Japan, January, 24–28, 2011. Tokyo: Mathematical Society of Japan. Adv. Stud. Pure Math. 82, 41-55 (2019).
Summary: In this paper, we define a reducibility for a triply periodic minimal surface, and study hyperelliptic minimal surfaces and trigonal minimal surfaces in terms of the reducibility. Restrictions on the topological type of the above minimal surfaces are given.
For the entire collection see [Zbl 1437.53042].

MSC:

53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
49Q05 Minimal surfaces and optimization

Keywords:

minimal surfaces; flat tori; Abel-Jacobi map
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\textit{T. Shoda}, Adv. Stud. Pure Math. 82, 41--55 (2019; Zbl 1453.53010)
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