충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제24권2호
  • /
  • Pages.313-317
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  • 2011
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  • 1226-3524(pISSN)
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  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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MINIMAL GRAPHS WITH PLANAR ENDS

  • Jin, Sun Sook (Department of Mathematics Education, Gongju National University of Education)
  • 투고 : 2011.03.16
  • 심사 : 2011.05.16
  • 발행 : 2011.06.30
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초록

In this article, we consider an unbounded minimal graph $M{\subset}R^3$ which is contained in a slab. Assume that ${\partial}M$ consists of two Jordan curves lying in parallel planes, which is symmetric with the reflection under a plane. If the asymptotic behavior of M is also symmetric in some sense, then we prove that the minimal graph is itself symmetric along the same plane.

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참고문헌

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  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