Existence of infinitely many free boundary minimal hypersurfaces

Zhichao Wang

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Existence of infinitely many free boundary minimal hypersurfaces

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arxiv 2001.04674 v3 pith:NSV2FFUK submitted 2020-01-14 math.DG math.APmath.GT

Existence of infinitely many free boundary minimal hypersurfaces

Zhichao Wang This is my paper

classification math.DG math.APmath.GT

keywords boundaryfreehypersurfacesminimalconjectureinfinitelymanyadaptions

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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.

Existence of infinitely many free boundary minimal hypersurfaces

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