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Funktsional. Anal. i Prilozhen., 1998, Volume 32, Issue 4, Pages 49–62 (Mi faa437)  

This article is cited in 32 scientific papers (total in 32 papers)

The Weierstrass Representation of Closed Surfaces in $\mathbb{R}^3$

I. A. Taimanov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences


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English version:
Functional Analysis and Its Applications, 1998, 32:4, 258–267

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UDC: 514.752.43+517.984
Received: 30.12.1997

Citation: I. A. Taimanov, “The Weierstrass Representation of Closed Surfaces in $\mathbb{R}^3$”, Funktsional. Anal. i Prilozhen., 32:4 (1998), 49–62; Funct. Anal. Appl., 32:4 (1998), 258–267

Citation in format AMSBIB
\by I.~A.~Taimanov
\paper The Weierstrass Representation of Closed Surfaces in $\mathbb{R}^3$
\jour Funktsional. Anal. i Prilozhen.
\yr 1998
\vol 32
\issue 4
\pages 49--62
\jour Funct. Anal. Appl.
\yr 1998
\vol 32
\issue 4
\pages 258--267

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    This publication is cited in the following articles:
    1. I. A. Taimanov, “The Weierstrass Representation of Spheres in $\mathbb R^3$, the Willmore Numbers, and Soliton Spheres”, Proc. Steklov Inst. Math., 225 (1999), 322–343  mathnet  mathscinet  zmath
    2. Helein, F, “Weierstrass representation of Lagrangian surfaces in four-dimensional space using spinors and quaternions”, Commentarii Mathematici Helvetici, 75:4 (2000), 668  crossref  mathscinet  zmath  isi
    3. I. A. Taimanov, “On two-dimensional finite-gap potential Schrödinger and Dirac operators with singular spectral curves”, Siberian Math. J., 44:4 (2003), 686–694  mathnet  crossref  mathscinet  zmath  isi  elib
    4. Landolfi, G, “New results on the Canham-Helfrich membrane model via the generalized Weierstrass representation”, Journal of Physics A-Mathematical and General, 36:48 (2003), 11937  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. I. A. Taimanov, “Dirac Operators and Conformal Invariants of Tori in 3-Space”, Proc. Steklov Inst. Math., 244 (2004), 233–263  mathnet  mathscinet  zmath
    6. A. E. Mironov, “Ierarkhiya uravnenii Veselova–Novikova i integriruemye deformatsii minimalnykh lagranzhevykh torov v $\mathbb CP^2$”, Sib. elektron. matem. izv., 1 (2004), 38–46  mathnet  mathscinet  zmath
    7. D. A. Berdinskii, I. A. Taimanov, “Surfaces in three-dimensional Lie groups”, Siberian Math. J., 46:6 (2005), 1005–1019  mathnet  crossref  mathscinet  zmath  isi
    8. Taimanov, IA, “Finite-gap theory of the Clifford torus”, International Mathematics Research Notices, 2005, no. 2, 103  crossref  mathscinet  zmath  isi  elib
    9. I. A. Taimanov, “Two-dimensional Dirac operator and the theory of surfaces”, Russian Math. Surveys, 61:1 (2006), 79–159  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. Matsutani, S, “Generalized Weierstrass relations and Frobenius reciprocity”, Mathematical Physics Analysis and Geometry, 9:4 (2006), 353  crossref  mathscinet  zmath  adsnasa  isi  scopus
    11. Taimanov, IA, “Surfaces in the four-space and the Davey-Stewartson equations”, Journal of Geometry and Physics, 56:8 (2006), 1235  crossref  mathscinet  zmath  adsnasa  isi  scopus
    12. Lawn, MA, “Immersions of Lorentzian surfaces in R-2,R-1”, Journal of Geometry and Physics, 58:6 (2008), 683  crossref  mathscinet  zmath  adsnasa  isi  scopus
    13. Bohle, C, “Discrete holomorphic geometry I. Darboux transformations and spectral curves”, Journal fur Die Reine und Angewandte Mathematik, 637 (2009), 99  crossref  mathscinet  zmath  isi  scopus
    14. Bohle, C, “The spectral curve of a quaternionic holomorphic line bundle over a 2-torus”, Manuscripta Mathematica, 130:3 (2009), 311  crossref  mathscinet  zmath  isi  elib  scopus
    15. Skovoroda, AA, “Plasma equilibrium in 3D magnetic confinement systems and soliton theory”, Plasma Physics Reports, 35:8 (2009), 619  crossref  adsnasa  isi
    16. Leschke K., Romon P., “Darboux transforms and spectral curves of Hamiltonian stationary Lagrangian tori”, Calculus of Variations and Partial Differential Equations, 38:1–2 (2010), 45–74  crossref  mathscinet  zmath  isi  scopus
    17. D. A. Berdinskii, “Ob odnom obobschenii funktsionala Uillmora dlya poverkhnostei v $\widetilde{SL}_2$”, Sib. elektron. matem. izv., 7 (2010), 140–149  mathnet  mathscinet
    18. Bohle Ch., “Constrained Willmore Tori in the 4-Sphere”, J Differential Geom, 86:1 (2010), 71–131  crossref  mathscinet  zmath  isi  elib  scopus
    19. Zakharov D., “A Discrete Analogue of the Dirac Operator and the Discrete Modified Novikov-Veselov Hierarchy”, Int Math Res Not, 2010, no. 18, 3463–3488  crossref  mathscinet  zmath  isi  elib  scopus
    20. I. A. Taimanov, “Singular spectral curves in finite-gap integration”, Russian Math. Surveys, 66:1 (2011), 107–144  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    21. D. V. Zakharov, “Weierstrass Representation for Discrete Isotropic Surfaces in $\mathbb{R}^{2,1}$, $\mathbb{R}^{3,1}$, and $\mathbb{R}^{2,2}$”, Funct. Anal. Appl., 45:1 (2011), 25–32  mathnet  crossref  crossref  mathscinet  zmath  isi
    22. Bohle Ch., Peters G.P., “Soliton Spheres”, Trans Amer Math Soc, 363:10 (2011), 5419–5463  crossref  mathscinet  zmath  isi  scopus
    23. McIntosh I., “The Quaternionic KP Hierarchy and Conformally Immersed 2-Tori in the 4-Sphere”, Tohoku Math J (2), 63:2 (2011), 183–215  crossref  mathscinet  zmath  isi  scopus
    24. Bohle Ch., Leschke K., Pedit F., Pinkall U., “Conformal Maps From a 2-Torus to the 4-Sphere”, J. Reine Angew. Math., 671 (2012), 1–30  crossref  mathscinet  zmath  isi  elib  scopus
    25. Moriya K., “A Condition for a Closed One-Form to Be Exact”, Adv. Appl. Clifford Algebr., 22:2 (2012), 433–448  crossref  mathscinet  zmath  isi  elib  scopus
    26. С. Bohle, I. A. Taimanov, “Spectral Curves for Cauchy–Riemann Operators on Punctured Elliptic Curves”, Funct. Anal. Appl., 47:4 (2013), 319–322  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    27. I. A. Taimanov, “The Moutard Transformation of Two-Dimensional Dirac Operators and Möbius Geometry”, Math. Notes, 97:1 (2015), 124–135  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    28. 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
    29. R. M. Matuev, I. A. Taimanov, “The Moutard Transformation of Two-Dimensional Dirac Operators and the Conformal Geometry of Surfaces in Four-Dimensional Space”, Math. Notes, 100:6 (2016), 835–846  mathnet  crossref  crossref  mathscinet  isi  elib
    30. P. G. Grinevich, S. P. Novikov, “Singular solitons and spectral meromorphy”, Russian Math. Surveys, 72:6 (2017), 1083–1107  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    31. Vaz Jr. Jayme, “Representation of Surfaces Using Spinor Operators”, J. Math. Phys., 60:2 (2019), 023509  crossref  mathscinet  zmath  isi  scopus
    32. Leschke K. Moriya K., “Simple Factor Dressing and the Lopez-Ros Deformation of Minimal Surfaces in Euclidean 3-Space”, Math. Z., 291:3-4 (2019), 1015–1058  crossref  mathscinet  zmath  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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