HIGHER CODIMENSION ISOPERIMETRIC PROBLEMSReport as inadecuate




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1 Department of Mathematics 2 CMLS - Centre de Mathématiques Laurent Schwartz

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.

Keywords : isoperimetric problem Constant mean curvature submanifold





Author: Rafe Mazzeo - Frank Pacard - Tatiana Zolotareva -

Source: https://hal.archives-ouvertes.fr/



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