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Funktsional'nyi Analiz i ego Prilozheniya, 2013, Volume 47, Issue 4, Pages 86–90
DOI: https://doi.org/10.4213/faa3131 (Mi faa3131) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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
Full-text PDF (148 kB) Citations (2)
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DOI: https://doi.org/10.4213/faa3131
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.
Keywords: Cauchy–Riemann operator, spectral curve, elliptic soliton.
Received: 25.12.2012
English version:
Functional Analysis and Its Applications, 2013, Volume 47, Issue 4, Pages 319–322
DOI: https://doi.org/10.1007/s10688-013-0039-3
Bibliographic databases:
Document Type: Article
UDC: 517.984.5
Language: Russian
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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  • https://www.mathnet.ru/eng/faa3131
  • https://doi.org/10.4213/faa3131
  • https://www.mathnet.ru/eng/faa/v47/i4/p86
    • This publication is cited in the following 2 articles:
    1. I. A. Taimanov, “Floquet–Bloch Functions on Non-simply Connected Manifolds, the Aharonov–Bohm Fluxes, and Conformal Invariants of Immersed Surfaces”, Proc. Steklov Inst. Math., 325 (2024), 280–291  mathnet  crossref  crossref  zmath
    2. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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    Full-text PDF :226
    References:81
    First page:31
     
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