论文标题
Ricci下限下的毛细管图的分裂定理
A splitting theorem for capillary graphs under Ricci lower bounds
论文作者
论文摘要
在本文中，我们研究了完整的Riemannian歧管$ M $的域$ω$定义的毛细管图，如果它具有持续的平均曲率，并且在$ \ partialω$上具有固定的dirichlet和neumann条件，则据说图形是毛细管。我们的主要结果是$ω$的分裂定理和对于具有非负RICCI曲率的一类流形的图形函数。作为推论，我们将毛细管图分类为产品空间中的全球lipschitz epigraphs或板块$ m = n \ times \ mathbb {r} $，其中$ n $的体积增长缓慢，非阴性ricci curvature，包括情况，包括$ m = \ mathbb = \ mathbb {r} $} $ nabb^$ mathb^33，c^33 c^r.ar c^r. c^r c^r. c^r c^r. r c^3 33 c.本文的技术核心是RICCI下限的歧管上正CMC图的新梯度估计。
In this paper, we study capillary graphs defined on a domain $Ω$ of a complete Riemannian manifold $M$, where a graph is said to be capillary if it has constant mean curvature and locally constant Dirichlet and Neumann conditions on $\partial Ω$. Our main result is a splitting theorem both for $Ω$ and for the graph function on a class of manifolds with nonnegative Ricci curvature. As a corollary, we classify capillary graphs over domains that are globally Lipschitz epigraphs or slabs in a product space $M = N \times \mathbb{R}$, where $N$ has slow volume growth and non-negative Ricci curvature, including the case $M = \mathbb{R}^2,\mathbb{R}^3$. A technical core of the paper is a new gradient estimate for positive CMC graphs on manifolds with Ricci lower bounds.
