Higher codimension isoperimetric problems

作者：Mazzeo Rafe^*; Pacard Frank; Zolotareva Tatiana

来源：Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, 2017, 17(3): 819-851.

We consider a variational problem for submanifolds Q subset of M with nonempty boundary partial derivative 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 problem; these concentrate near the critical points of a certain curvature function.

• 出版日期2017