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SOME REMARKS ON TOTAL CURVATURE OF A MINIMAL GRAPH

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초록

In this paper we discuss bounds for the total curvature of nonparametric minimal surfaces by using the properties of planar harmonic mappings.

Abstract

In this paper we discuss bounds for the total curvature of nonparametric minimal surfaces by using the properties of planar harmonic mappings.

참고문헌 (9)

  1. D. Bshouty, "On the Gauss map of minimal graphs", Complex Var. Theory Appl, 48(4), pp.339~346 (2003)
  2. J. G. Clunie, "Harmonic univalent functions", Ann. Acad. Sci. Fenn. Ser. A I, 9, pp.3~25 (1984)
  3. F. Colonna, "The Bloch constant of bounded analytic functions", J. London Math. Soc, 36(1), pp.95~101 (1987)
  4. U. Dierkes, "Minimal Surfaces I. Boundary Value Problems", Grundlehren der Math. Wiss, 295 (1992), Springer-Verlag
  5. P. Duren, "Harmonic Mappings in the Plane", Cambridge Tracts in Mathematics, 156 (2004), Cambridge University Press
  6. G. M. Goluzin, "Geometric Theory of Functions of a Complex Variable, GITTL, Moscow, 1952", Transl. Math. Monographs, 26 (1969), Amer. Soc
  7. E. Heinz, "¨Uber die Losungen der Minimalflachengleichung, Nachr. Akad. Wiss. G¨ttingen. Math.-Phys. Kl. Math.-Phys.-Chem. Abt", pp.51~56 (1952)
  8. E. Reich, "An inequality for subordinate analytic functions", Pacific J. Math, 4(2), pp.259~274 (1954)
  9. S. Yamashita, "Spherical derivative of meromorphic function with image of finite spherical area", J. Inequal. Appl, 5(2), pp.191~199 (2000)

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