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THE SECOND DERIVATIVE OF THE ENERGY FUNCTIONAL

Kim, Hwa-Jeong

  • Received : 2012.02.09
  • Accepted : 2012.02.24
  • Published : 2012.06.25

Abstract

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.

Keywords

Minimal surfaces;Plateau's problem

References

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Cited by

  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

Acknowledgement

Supported by : Hannam University