Communications in Analysis and Geometry

Volume 31 (2023)

Number 5

Free boundary minimal hypersurfaces with least area

Pages: 1177 – 1215

DOI: https://dx.doi.org/10.4310/CAG.2023.v31.n5.a4

Authors

Qiang Guang (Department of Mathematics, University of California Santa Barbara, Calif., USA)

Zhichao Wang (Beijing International Center for Mathematical Research, Peking University, Beijing, China)

Xin Zhou (Department of Mathematics, University of California Santa Barbara, Santa Barbara, CA, USA; Department of Mathematics, Cornell University, Ithaca, NY, USA)

Abstract

In this paper, we prove the existence of the free boundary minimal hypersurface of least area in compact manifolds with boundary. Such a hypersurface can be viewed as the ground state of the volume spectrum introduced by Gromov. Moreover, we characterize the orientation and Morse index of them.

Full Text (PDF format)

Received 6 January 2020

Accepted 15 April 2021

Published 16 July 2024