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On the second inner variation of the Allen-Cahn Functional and its applications

Authors
  • Le, Nam Q.
Type
Preprint
Publication Date
Sep 28, 2010
Submission Date
Sep 28, 2010
Source
arXiv
License
Yellow
External links

Abstract

In this paper, we study the relation between the second inner variations of the Allen-Cahn functional and its Gamma-limit, the area functional. Our result implies that the Allen-Cahn functional only approximates well the area functional up to the first order. However, as an application of our result, we prove, assuming the single-multiplicity property of the limiting energy, that the Morse indices of critical points of the Allen-Cahn functional are bounded from below by the Morse index of the limiting minimal hypersurface.

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