论文标题
存在无限的许多自由边界最小的超曲面
Existence of infinitely many free boundary minimal hypersurfaces
论文作者
论文摘要
在本文中，我们证明，在任何紧凑的riemannian歧管中，尺寸至少为3，最多有7个，几乎有许多几乎适当地嵌入的自由边界最小的超曲面。这解决了Yau猜想的免费边界版本。该证明使用了A. Song的作品的改编和Marques-neves的早期作品，以解决Yau的猜想，以及Li-Zhou的规律定理，用于自由边界最小的最小效果。
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.
