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Funktsional. Anal. i Prilozhen., 2013, Volume 47, Issue 4, Pages 86–90 (Mi faa3131)  

This article is cited in 1 scientific paper (total in 1 paper)

Brief communications

Spectral Curves for Cauchy–Riemann Operators on Punctured Elliptic Curves

С. Bohlea, I. A. Taimanovb

a Mathematisches Institut, Universität Tübingen
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

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 $\mathbb{R}^3$. It turns out that these curves coincide with the spectral curves of certain elliptic KP solitons studied by Krichever.

Keywords: Cauchy–Riemann operator, spectral curve, elliptic soliton

DOI: https://doi.org/10.4213/faa3131

Full text: PDF file (148 kB)
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English version:
Functional Analysis and Its Applications, 2013, 47:4, 319–322

Bibliographic databases:

UDC: 517.984.5
Received: 25.12.2012

Citation: С. Bohle, I. A. Taimanov, “Spectral Curves for Cauchy–Riemann Operators on Punctured Elliptic Curves”, Funktsional. Anal. i Prilozhen., 47:4 (2013), 86–90; Funct. Anal. Appl., 47:4 (2013), 319–322

Citation in format AMSBIB
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\paper Spectral Curves for Cauchy--Riemann Operators on Punctured Elliptic Curves
\jour Funktsional. Anal. i Prilozhen.
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\vol 47
\issue 4
\pages 86--90
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  • https://doi.org/10.4213/faa3131
  • http://mi.mathnet.ru/eng/faa/v47/i4/p86

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Bohle Ch. Taimanov I.A., “Euclidean Minimal Tori With Planar Ends and Elliptic Solitons”, Int. Math. Res. Notices, 2015, no. 14, 5907–5932  crossref  mathscinet  zmath  isi  elib  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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