Free boundary minimal hypersurfaces with least area

Abstract

In this paper, we prove the existence of the free boundary minimal hypersurface of least area in compact manifolds with boundary. Such 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.

arXiv comment32 pages, 6 figures

References in corpus (5)

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Cited by in corpus (3)

• Free boundary minimal surfaces in the unit ball : recent advances and open questions
• Existence of infinitely many free boundary minimal hypersurfaces
• Locally Maximizing Metric of Width on Manifolds with Boundary