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The infinitesimal variation of the spin abelian differentials and periodic minimal surfaces. (English) Zbl 0914.58007

The author proves that there is a countable number of genus \(g\), \(g>2\), compact minimal immersed surfaces in any flat real \(3\)-torus. Moreover, he studies the locus corresponding to proper triply periodic minimal surfaces in \(M_g\), the moduli space of genus \(g\) compact connected Riemann surfaces and shows that its closure contains a vanishing thetanull if \(g>2\) and the locus of the smooth plane quintics is \(g=6\).
Reviewer: W.Mozgawa (Lublin)

MSC:

58E12 Variational problems concerning minimal surfaces (problems in two independent variables)
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