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EXISTENCE OF MINIMAL SURFACES WITH PLANAR ENDS

진선숙
한국수학교육학회|2010.11|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제17권 제4호|pp. 299-306

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참고문헌

키워드

fluxtorqueaxisminimal surfaces
주제분류수학

초록

In this article we consider axes of a complete embedded minimal surface in R³ of finite total curvature, and then prove that there is no planar ends at which the Gauss map have the minimum branching order if the minimal surface has a single axis.

Abstract

In this article we consider axes of a complete embedded minimal surface in R³ of finite total curvature, and then prove that there is no planar ends at which the Gauss map have the minimum branching order if the minimal surface has a single axis.

참고문헌 (7)

  1. Y. Fang, "Lectures on minimal surfaces in R3", Proc. centre for Math. and its Applications, 통권 : 35 (1996), Australian Nat. Univ
  2. D.A. Hoffman, "Complete embedded minimal surfaces of finite total curva-ture, Geometry V, Chapter 1", pp.7~93 (1997), Springer
  3. D.A. Hoffman, "The strong halfspace theorem for minimal surfaces", Invent. Math, 101, pp.373~377 (1990)
  4. S.S. Jin, "A minimal surface of R3 with planar ends", Kyushu J. of Math, 55(2), pp.351~369 (2001)
  5. R. Kusner, "Global geometry of extremal surfaces in three-space", 박사, pp.1988
  6. R. Osserman, "A survey of minimal surfaces vol.1" (1989), Cambrige Univ. Press
  7. R. Schoen, "Uniqueness, symmetry and embeddedness of minimal surfaces", J. Diff. Geom, 18, pp.701~809 (1983)

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