Geodesic
Two-dimensional Dirac operator and the theory of surfaces
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 61 (2006) no. 1, pp. 79-159

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A survey is given of the Weierstrass representations of surfaces in three- and four-dimensional spaces, their applications to the theory of the Willmore functional, and related problems in the spectral theory of the two-dimensional Dirac operator with periodic coefficients. 
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     author = {I. A. Taimanov},
     title = {Two-dimensional {Dirac} operator and the theory of surfaces},
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I. A. Taimanov. Two-dimensional Dirac operator and the theory of surfaces. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 61 (2006) no. 1, pp. 79-159. http://geodesic.mathdoc.fr/item/RM_2006_61_1_a2/