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Articles

Minimal surfaces associated with orthogonal polynomials

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Pages 529-549 | Received 17 Jan 2019, Accepted 03 Dec 2019, Published online: 04 Sep 2020

References

  • F.F. Chen, Introduction to plasma physics and controlled fusion, (Springer, 1984).
  • A.S. Davydov et al., Solitons in molecular systems, (Springer, 1985).
  • F. David, P. Ginsparg and J. Zinn-Justin, Fluctuating geometries in statistical mechanics and field theory, (Elsevier-North-Holland, Amsterdam, 1996).
  • G. Landolfi, On the Canham–Helfrich membrane model, Journal of Physics A: Mathematical and General, 36 (4) (2003) 699–715.
  • D.J. Gross, T. Piran and S. Weinberg, Two dimensional quantum gravity and random surfaces, (World Scientific Singapore, 1992).
  • D.R. Nelson, T. Piran and S. Weinberg, Statistical mechanics of membranes and surfaces, (World Scientific, 2004).
  • Z.-C. Ou-Yang, J.-X. Liu, Y.-Z. Xie and X. Yu-Zhang, Geometric methods in the elastic theory of membranes in liquid crystal phases, (World Scientific, 1999).
  • J. Polchinski and A. Strominger, Effective string theory, Physical review letters, 67 (13) (1991) p. 1681. doi: 10.1103/PhysRevLett.67.1681
  • S. Safran, Statistical thermodynamics of surfaces, interfaces, and membranes, (CRC Press, 2018).
  • A. Sommerfeld, Lectures on theoretical physics, Vol. 1-3, (Academic Press, 1964).
  • A.I. Bobenko, Surfaces in terms of 2 by 2 matrices. Old and new integrable cases, Harmonic maps and integrable systems, (1994) 83–127.
  • C. Brezinski, A.P. Magnus, A. Ronveaux, A. Draux and P. Maroni, Polynômes orthogonaux et applications, (Springer-Verlag, Berlin, 1984).
  • G.E. Andrews, R. Askey and R. Roy, Special functions, (Cambridge university press, 2000).
  • F. Olver, Asymptotics and special functions, (Academic press, New York, 1974).
  • M. Abramowitz and I.A. Segun, Handbook of Mathematical Functions, (Dover, New York, 1965).
  • E.D. Rainville, Special functions, (The MacMillan Company, New York, 1960).
  • A. Doliwa and A.M. Grundland, Minimal surfaces in the soliton surface approach, arXiv ID: 1511.02173 (2015).
  • A.I. Bobenko and U. Eitner, Painlevéequations in the differential geometry of surfaces, (Springer-Verlag, Berlin, 2000).
  • K. Weierstrass, Fortsetzung der untersuchung über die minimalflachen, Mathematische Werke, 3 (1866) 219–248.
  • A. Enneper, Analytisch-geometrische untersuchungen nachr, Königl. Gesell. Wissensch. Georg– Augusts-Univ. Göttingen, 12 (1868) 258–277.
  • A. Sym, Soliton surfaces, Littere al Nuovo Cimento 33 (1982) 394–400, which also mentions J. Tafel contribution. doi: 10.1007/BF02725614
  • A. Sym, Soliton surfaces and their applications (soliton geometry from spectral problems), Geometric aspects of the Einstein equations and integrable systems, Lecture notes in Physics, 239 (1985) 154–231. doi: 10.1007/3-540-16039-6_6
  • B.G. Konopelchenko, Induced surfaces and their integrable dynamics, Studies in applied mathematics, 96 (1) (1996) 9–51. doi: 10.1002/sapm19969619
  • A. Bobenko, Surfaces of constant mean curvature and integrable equations, Uspekhi Mat. Nauk, 46 (4(280)) (1991) 3–42.
  • A.M. Grundland and I. Yurdusen, On analytic descriptions of two-dimensional surfaces associated with the CP(N-1) sigma model, J. Phys. A: Math. Theor., 42 (2009) p. 172001. doi: 10.1088/1751-8113/42/17/172001
  • J.L. Cieśliński, A geometric interpretation of the spectral parameter for surfaces of constant mean curvature, Journal of Nonlinear Mathematical Physics, 13 (4) (2006) 507–515. doi: 10.2991/jnmp.2006.13.4.5
  • Wolfram Research, Exponential integral, accessed in november 2018. URL: http://functions.wolfram.com/06.35.02.0001.01.

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