Abstract
We show that one can define a spectral curve for the Cauchy-Riemann operator on a punctured elliptic curve under appropriate boundary conditions. The algebraic curves thus obtained arise, for example, as irreducible components of the spectral curves of minimal tori with planar ends in ℝ3. It turns out that these curves coincide with the spectral curves of certain elliptic KP solitons studied by Krichever.
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References
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 47, No. 4, pp. 86–90, 2013
Original Russian Text Copyright © by C. Bohle and I. A. Taimanov
This work was supported by the Hausdorff Institute of Mathematics in Bonn. The first author (C.B.) acknowledges the support of DFG Sfb/Tr grant 71 (“Geometric Partial Differential Equations”), and the second author (I.A.T.) acknowledges the support of the Presidium of RAS program “Fundamental Problems of Nonlinear Dynamics in Mathematical and Physical Sciences.”
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Bohle, C., Taimanov, I.A. Spectral curves for Cauchy-Riemann operators on punctured elliptic curves. Funct Anal Its Appl 47, 319–322 (2013). https://doi.org/10.1007/s10688-013-0039-3
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DOI: https://doi.org/10.1007/s10688-013-0039-3