Pirola, Gian Pietro The infinitesimal variation of the spin abelian differentials and periodic minimal surfaces. (English) Zbl 0914.58007 Commun. Anal. Geom. 6, No. 3, 393-426 (1998). 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) Cited in 7 Documents MSC: 58E12 Variational problems concerning minimal surfaces (problems in two independent variables) Keywords:spin abelian differentials; proper triply periodic minimal surfaces; theta divisor PDFBibTeX XMLCite \textit{G. P. Pirola}, Commun. Anal. Geom. 6, No. 3, 393--426 (1998; Zbl 0914.58007) Full Text: DOI