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

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

1997-10-20

arxiv.org/abs/dg-ga/9710020v3

Functional Anal. Appl. 32:4 (1998), 49--62.

Mathematics

Differential Geometry

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

Scientific paper

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 $\geq 1$ 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.

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