호남수학학술지 (Honam Mathematical Journal)

  • 제34권2호
  • /
  • Pages.191-198
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  • 2012
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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THE SECOND DERIVATIVE OF THE ENERGY FUNCTIONAL

  • 투고 : 2012.02.09
  • 심사 : 2012.02.24
  • 발행 : 2012.06.25
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초록

Minimal surfaces with given boundaries are the solutions of Plateau's problem. In studying the calculus of variations for the minimal surfaces, the functional ${\varepsilon}$, corresponding to the energy of surfaces, is introduced in [Ki09]. In this paper we derive a formula for the second derivative of ${\varepsilon}$, which is necessary for further theories of the calculus of variations.

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참고문헌

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  10. Struwe, M.:, Plateau's Problem and the calculus of variations, Princeton U.P. 1998.
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피인용 문헌

  1. A NOTE ON THE JACOBI FIELDS ON MANIFOLDS vol.38, pp.2, 2016, https://doi.org/10.5831/HMJ.2016.38.2.385
  2. Morse theory for minimal surfaces in manifolds vol.54, pp.2, 2018, https://doi.org/10.1007/s10455-018-9601-9