충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제23권2호
  • /
  • Pages.251-256
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  • 2010
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  • 1226-3524(pISSN)
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  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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SYMMETRY OF MINIMAL GRAPHS

  • Jin, Sun Sook (Department of Mathematics Education Gongju National University of Education)
  • 투고 : 2010.01.25
  • 심사 : 2010.04.23
  • 발행 : 2010.06.30
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초록

In this article, we consider a minimal graph in $R^3$ which is bounded by a Jordan curve and a straight line. Suppose that the boundary is symmetric with the reflection under a plane, then we will prove that the minimal graph is itself symmetric under the reflection through the same plane.

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참고문헌

  1. M. Anderson, Curvature estimates for minimal surfaces in 3-manifolds, Ann. Scient. Ec. Norm. Sup. 18 (1985), 89-105. https://doi.org/10.24033/asens.1485
  2. U. Dierkes, S. Hildebrandt, A. Kuster, and O. Wohlrab, Minimal Surfaces 1, Springer-Verlag, 1992.
  3. Yi Fang, On minimal annuli in a slab, Comm. Math. Helv. 69 (1994), 417-430. https://doi.org/10.1007/BF02564495
  4. S. S. Jin, A minimal surface of $R^3$ with planar ends, Kyushu J. of Math. 55-2 (2001), 351-368. https://doi.org/10.2206/kyushujm.55.351
  5. W. Meeks, J. Perez. Conformal properties in classical minimal surface theory. Surveys in Differential Geometry, Volume IX: International Press, 2004.
  6. R. Osserman, A survey of minimal surfaces, vol.1. Cambrige Univ. Press, New York, 1989.
  7. R. Schoen, Uniqueness, symmetry and embeddedness of minimal surfaces, J. Diff. Geom. 18 (1983), 701-809. https://doi.org/10.4310/jdg/1214438178
  8. M. Shiffman, On surfaces of stationary area bounded by two circles, or convex curves, in parallel planes. Ann. Math. 63 (1956), 77-90. https://doi.org/10.2307/1969991