论文标题
层次结构有限指数CMC表面
Hierarchy structures in finite index CMC surfaces
论文作者
论文摘要
给定$ \ varepsilon_0> 0 $，$ i \ in \ mathbb {n} \ cup \ {0 \ {0 \} $和$ k_0，h_0 \ geq0 $，让$ x $成为完整的riemannian riemannian $ 3 $ -MANIFOLD $ 3 $ -MANIFOLD，并带有Inpotivity radius $ \ mbox $ \ mbox {preem and preem and preem and preem and preem and preem and preem and preem and preem and preem and preem and preem and preem and preem and。绝对的截面曲率最多$ k_0 $，让$ m \ looparrowright x $是[0，h_0] $ in [0，h_0] $的完整沉浸式表面，最多是$ i $。对于这种$ M \ looparrowright x $，我们证明了结构定理1.2，它描述了如何在本地以$ $ m $的最大$ i $ $ $ m $ $ $ m $进行的有趣的环境几何形状，其中第二个基本形式的规范以较大的本地最大值为单位。
Given $\varepsilon_0>0$, $I\in \mathbb{N}\cup \{0\}$ and $K_0,H_0\geq0$, let $X$ be a complete Riemannian $3$-manifold with injectivity radius $\mbox{Inj}(X)\geq \varepsilon_0$ and with the supremum of absolute sectional curvature at most $K_0$, and let $M \looparrowright X$ be a complete immersed surface of constant mean curvature $H\in [0,H_0]$ with index at most $I$. For such $M \looparrowright X$, we prove Structure Theorem 1.2 which describes how the interesting ambient geometry of the immersion is organized locally around at most $I$ points of $M$ where the norm of the second fundamental form takes on large local maximum values.
