The infinitesimal variation of the spin abelian differentials and periodic minimal surfaces
Gian Pietro Pirola · Communications in Analysis and Geometry · 1998
The infinitesimal variation of the spin abelian differentials and periodic minimal surfacesGlAN PlETRO PlROLA 1We study the first order variation of some abelian differentials closely related with the theory of triply periodic minimal surfaces.The main application is an existence result: We prove that there is a countable number of genus g, g > 2, compact minimal immersed surfaces in any flat real 3 torus.We also study the locus corresponding to proper triply periodic minimal surfaces in Mg y the moduli space of genus g compact connected Riemann surfaces: We show that its closure contains the thetanull divisor if g > 2 and the locus of the smooth plane quintics if g = 6.