Mean curvature and variational theory

  • Xin Zhou

    Department of Mathematics, Cornell University, Ithaca, NY 14853, USA, and Department of Mathematics, University of California Santa Barbara, Santa Barbara, CA 93106, USA
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In this article, we survey recent progress on the variational theory related to mean curvature. We will discuss the Morse theory of minimal hypersurfaces with an emphasis on the Multiplicity One Conjecture, generic spatial distributions of minimal hypersurfaces, variational theory for constant mean curvature (CMC) surfaces, and variational theory for minimal surfaces with free boundary.