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Comparison between second variation of area and second variation of energy of a minimal surface
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Ejiri, Norio and Micallef, Mario (2008) Comparison between second variation of area and second variation of energy of a minimal surface. Advances in Calculus of Variations, Vol.1 (No.3). pp. 223-239. doi:10.1515/ACV.2008.009 ISSN 1864-8258.
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Official URL: http://dx.doi.org/10.1515/ACV.2008.009
Abstract
We show that the difference between the Morse index of a closed minimal surface as a critical point of the area functional and its Morse index as a critical point of the energy is at most the real dimension of Teichmüller space. This enables us to bound the index of a closed minimal surface in an arbitrary Riemannian manifold by the area and genus of the surface, and the dimension and geometry of the ambient manifold. Our method also yields surprisingly good upper bounds on the index of a minimal surface of finite total curvature in Euclidean space of any dimension.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Advances in Calculus of Variations | ||||
Publisher: | Walter de Gruyter GmbH & Co. KG | ||||
ISSN: | 1864-8258 | ||||
Official Date: | November 2008 | ||||
Dates: |
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Volume: | Vol.1 | ||||
Number: | No.3 | ||||
Page Range: | pp. 223-239 | ||||
DOI: | 10.1515/ACV.2008.009 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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