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Uspekhi Mat. Nauk, 1991, Volume 46, Issue 4(280), Pages 3–42 (Mi umn4628)  

This article is cited in 28 scientific papers (total in 28 papers)

Constant mean curvature surfaces and integrable equations

A. I. Bobenko


Full text: PDF file (2049 kB)
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English version:
Russian Mathematical Surveys, 1991, 46:4, 1–45

Bibliographic databases:

UDC: 513+517.9
MSC: 30F10, 32J15

Citation: A. I. Bobenko, “Constant mean curvature surfaces and integrable equations”, Uspekhi Mat. Nauk, 46:4(280) (1991), 3–42; Russian Math. Surveys, 46:4 (1991), 1–45

Citation in format AMSBIB
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\by A.~I.~Bobenko
\paper Constant mean curvature surfaces and integrable equations
\jour Uspekhi Mat. Nauk
\yr 1991
\vol 46
\issue 4(280)
\pages 3--42
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\transl
\jour Russian Math. Surveys
\yr 1991
\vol 46
\issue 4
\pages 1--45
\crossref{https://doi.org/10.1070/RM1991v046n04ABEH002826}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Christian Jaggy, “On the classification of constant mean curvature tori in ℝ3”, Comment Math Helv, 69:1 (1994), 640  crossref  mathscinet  zmath  isi
    2. I McIntosh, Nonlinearity, 7:1 (1994), 85  crossref
    3. A. P. Veselov, S. P. Novikov, “Exactly soluble periodic two-dimensional Schrödinger operators”, Russian Math. Surveys, 50:6 (1995), 1316–1317  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. G. G. Varzugin, E. Sh. Gutshabash, V. D. Lipovskii, “Boundary-value problem for the two-dimensional stationary Heisenberg magnet with non-trivial background. II”, Theoret. and Math. Phys., 104:3 (1995), 1166–1177  mathnet  crossref  mathscinet  zmath  isi
    5. A. O. Smirnov, “3-Elliptic solutions of the sine-Gordon equation”, Math. Notes, 62:3 (1997), 368–376  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. S. P. Novikov, I. A. Dynnikov, “Discrete spectral symmetries of low-dimensional differential operators and difference operators on regular lattices and two-dimensional manifolds”, Russian Math. Surveys, 52:5 (1997), 1057–1116  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    7. E. Sh. Gutshabash, V. D. Lipovskii, S. S. Nikulichev, “Nonlinear $\sigma$-model in a curved space, gauge equivalence, and exact solutions of $(2+0)$-dimensional integrable equations”, Theoret. and Math. Phys., 115:3 (1998), 619–638  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. Ian McIntosh, “On the existence of superconformal 2-tori and doubly periodic affine Toda fields”, Journal of Geometry and Physics, 24:3 (1998), 223  crossref
    9. Atsushi Fujioka, Jun-ichi Inoguchi, “Bonnet Surfaces with Constant Curvature”, Results. Math, 33:3-4 (1998), 288  crossref
    10. YURI B. SURIS, “INTEGRABLE DISCRETIZATIONS FOR LATTICE SYSTEM: LOCAL EQUATIONS OF MOTION AND THEIR HAMILTONIAN PROPERTIES”, Rev. Math. Phys, 11:06 (1999), 727  crossref
    11. L. A. Masal'tsev, “Joachimsthal surfaces in $S^3$”, Math. Notes, 67:2 (2000), 176–182  mathnet  crossref  crossref  mathscinet  zmath  isi
    12. Bobenko, AI, “Painlevé equations in the differential geometry of surfaces”, Painleve Equations in Differential Geometry of Surfaces H), 1753 (2000), 1  crossref  mathscinet  isi
    13. Chr.C. Beneki, G. Kaimakamis, B.J. Papantoniou, “Helicoidal surfaces in three-dimensional Minkowski space”, Journal of Mathematical Analysis and Applications, 275:2 (2002), 586  crossref
    14. Magdalena Toda, “Initial Value Problems of the sine-Gordon Equation and Geometric Solutions”, Ann Global Anal Geom, 27:3 (2005), 257  crossref  mathscinet  zmath  isi  elib
    15. 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
    16. J.-H. Eschenburg, P. Quast, “Pluriharmonic maps into Kähler symmetric spaces and SYM’s formula”, Math Z, 264:2 (2009), 469–481  crossref  mathscinet  isi
    17. J.-H. Eschenburg, P. Quast, “Pluriharmonic maps into Kähler symmetric spaces and Sym's formula”, Erratum to: Math. Z. DOI 10.1007/s00209-008-0472-9, Math. Z., 264:2 (2009), 483–484  crossref  mathscinet
    18. Peter Quast, “Twistor fibrations over Hermitian symmetric spaces and harmonic maps”, Differential Geometry and its Applications, 27:1 (2009), 1  crossref
    19. Gökçe Başar, Gerald V. Dunne, “Gross-Neveu models, nonlinear Dirac equations, surfaces and strings”, J. High Energ. Phys, 2011:1 (2011)  crossref
    20. Basar G., Dunne G.V., “Gross-Neveu models, nonlinear Dirac equations, surfaces and strings”, Journal of High Energy Physics, 2011, no. 1, 127  isi
    21. Bohle Ch., Peters G.P., “Soliton Spheres”, Trans Amer Math Soc, 363:10 (2011), 5419–5463  crossref  isi
    22. Berdinskii D.A., “O minimalnykh poverkhnostyakh v gruppe geizenberga”, Vestnik Kemerovskogo gosudarstvennogo universiteta, 2011, no. 3-1, 34–38  elib
    23. R. Pacheco, “Immersed surfaces in Lie algebras associated to primitive harmonic maps”, Geom Dedicata, 2012  crossref
    24. Sebastian Heller, “Lawson’s genus two surface and meromorphic connections”, Math. Z, 2012  crossref
    25. Sébastien Cartier, “SYM–Bobenko formula for minimal surfaces in Heisenberg space”, Comptes Rendus Mathematique, 2013  crossref
    26. P. G. Grinevich, A. E. Mironov, S. P. Novikov, “On the non-relativistic two-dimensional purely magnetic supersymmetric Pauli operator”, Russian Math. Surveys, 70:2 (2015), 299–329  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    27. Bohle Ch., Taimanov I.A., “Euclidean Minimal Tori With Planar Ends and Elliptic Solitons”, no. 14, 2015, 5907–5932  crossref  isi
    28. 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
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