The Weierstrass representation of closed surfaces in $R^3$

Abstract

In the present paper which a sequel to dg-ga/9511005 and dg-ga//9610013 a global Weierstrass representation of an arbitrary closed oriented surface of genus $\ge 1$ in the the three-space is constructed. The Weierstrass spectrum of a torus immersed into $R^3$ is introduced and finite-zone planes as well as finite-zone solutions to the modified Novikov-Veselov equations are constructed.

15 pages, LaTeX; Preprint no. 291, SFB 288, TU-Berlin

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