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HIGHER CODIMENSION ISOPERIMETRIC PROBLEMS

Abstract : We consider a variational problem for submanifolds Q ⊂ M with nonempty boundary ∂Q = K. We propose the definition that the boundary K of any critical point Q have constant mean curvature, which seems to be a new perspective when dim Q < dim M . We then construct small nearly-spherical solutions of this higher codimension CMC prob-lem; these concentrate near the critical points of a certain curvature function.
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https://hal.archives-ouvertes.fr/hal-01118388
Contributor : Tatiana Zolotareva <>
Submitted on : Sunday, February 22, 2015 - 4:22:57 PM
Last modification on : Thursday, March 5, 2020 - 6:30:25 PM
Document(s) archivé(s) le : Saturday, September 12, 2015 - 6:40:30 PM

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  • HAL Id : hal-01118388, version 1
  • ARXIV : 1502.06746

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Rafe Mazzeo, Frank Pacard, Tatiana Zolotareva. HIGHER CODIMENSION ISOPERIMETRIC PROBLEMS. 2015. ⟨hal-01118388⟩

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