Elliptic Functions, Green Functions and the Mean Field Equations on Tori
نویسندگان
چکیده
We show that the Green functions on flat tori can have either 3 or 5 critical points only. There does not seem to be any direct method to attack this problem. Instead, we have to employ sophisticated non-linear partial differential equations to study it. We also study the distribution of number of critical points over the moduli space of flat tori through deformations. The functional equations of special theta values provide important inequalities which lead to a solution for all rhombus tori. The general picture is also emerged, though some of the necessary technicality is still to de developed.
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تاریخ انتشار 2006