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arXiv · 1502.06746

Higher codimension isoperimetric problems

Rafe Mazzeo·Frank Pacard·Tatiana Zolotareva
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Abstract

We consider a variational problem for submanifolds Q $\subset$ M with nonempty boundary $\partial$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 \textless{} 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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Rafe Mazzeo, Frank Pacard, Tatiana Zolotareva. 2015-02-24. Higher codimension isoperimetric problems. https://arxiv.org/abs/1502.06746

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