Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 291

The Weierstrass representation of closed surfaces in ${f R}^3$

I. A. Taimanov

In the present paper which a sequel to [19] and [20] a global Weierstrass representation of an arbitrary closed oriented surface of genus $geq 1$ in the the three-space is constructed. The Weierstrass spectrum of a torus immersed into ${f R}^3$ is introduced and finite-zone planes as well as finite-zone solutions to the modified Novikov-Veselov equations are constructed.

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