Existence of infinitely many free boundary minimal hypersurfaces
arXiv:2001.04674
Abstract
In this paper, we prove that in any compact Riemannian manifold with smooth boundary, of dimension at least 3 and at most 7, there exist infinitely many almost properly embedded free boundary minimal hypersurfaces. This settles the free boundary version of Yau's conjecture. The proof uses adaptions of A. Song's work and the early works by Marques-Neves in their resolution to Yau's conjecture, together with Li-Zhou's regularity theorem for free boundary min-max minimal hypersurfaces.
arXiv comment30 pages, 2 figures; references updated; add Lemma 2.13 to exclude the mass concentration at corners; to appear in JDG
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