대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제20권3호
  • /
  • Pages.511-520
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  • 2005
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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NON-COMPACT DOUGLAS-PLATEAU PROBLEM BOUNDED BY A LINE AND A JORDAN CURVE

  • JIN, Sun-Sook (Major in Mathematics and Applies Mathematics College of Electronics and Information Kyung Hee University)
  • 발행 : 2005.07.01
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초록

In this article, we prove the existence of a minimal annulus bounded by a Jordan curve and a straight line.

키워드

참고문헌

  1. R. Courant, Dirichlet's principle, conformal mapping and minimal surfaces, New York, Interscience, 1950
  2. U. Dierkes, S. Hildebrandt, A. Kuster, and O. Wohlrab, Minimal Surfaces 1, Springer-Verlag, 1992
  3. J. Douglas, Solution to the problem of Plateau, Trans. Amer. Math. Soc. 33 (1931), 263-321 https://doi.org/10.2307/1989472
  4. J. Douglas,The problem of Plateau for two contours, J. Math. Phys. Massachusetts Inst. of Tech. 10 (1930/31), 315-359
  5. Yi Fang, On minimal annuli in a slab, Comm. Math. Helv. 69 (1994), 417-430 https://doi.org/10.1007/BF02564495
  6. Yi Fang and Jenn-Fang Hwang, Curvature estimates for minimal annuli and noncompact Douglas-Plateau problem, Comm. Anal. Geom. 8 (2000), no. 4, 871-904 https://doi.org/10.4310/CAG.2000.v8.n4.a6
  7. H. Jenkins and J. Serrin, Variational problems of minimal surface type, 2, Boundary value problems for the minimal surface equation, Arch. Rational Mech. Anal. 21 (1966),321-342
  8. F. J. Lopez and F. Wei, Properly immersed minimal discs bounded by straight lines, Math. Ann. 318 (2000), 667-706 https://doi.org/10.1007/s002080000134
  9. J. Perez and A. Ros, Properly embedded minimal annuli bounded by a convex curve, Journal de l'Institut Mathematique de Jussieu 1 (2002), no. 2, 293-305 https://doi.org/10.1017/S1474-748002000075
  10. B. Riemann, Uber die Fliiche vom kleinsten Inhalt bei gegebener Begrebzung, Abh. Konigl, d. Wiss. Gottingen, Mathern. Cl. 13 (1867), 3-52
  11. . Tomi and R. Ye, The exterior plateau problem, Math. Z. 205 (1990), 233-245 https://doi.org/10.1007/BF02571238