论文标题
双曲线空间中的平均曲率和几乎恒定平均曲率的气泡
Bubbles with constant mean curvature, and almost constant mean curvature, in the hyperbolic space
论文作者
论文摘要
给定常数$ k> 1 $，让$ z $成为半径$ \ textrm {artanh}（k^{ - 1}）$的圆形领域的家族$ \ mathbb {h}^3 $，以便任何$ z $中的任何sphere in $ z $中的任何sphere in $ z $都有平均弯曲$ k $。我们证明了涉及歧管$ z $的至关重要的非等级结果。作为一个应用程序，我们在$ \ mathbb {h}^3 $上的规定功能$ ϕ $上提供足够的条件每个点。
Given a constant $k>1$, let $Z$ be the family of round spheres of radius $\textrm{artanh}(k^{-1})$ in the hyperbolic space $\mathbb{H}^3$, so that any sphere in $Z$ has mean curvature $k$. We prove a crucial nondegeneracy result involving the manifold $Z$. As an application, we provide sufficient conditions on a prescribed function $ϕ$ on $\mathbb{H}^3$, which ensure the existence of a ${\cal C}^1$-curve, parametrized by $\varepsilon\approx 0$, of embedded spheres in $\mathbb{H}^3$ having mean curvature $k +\varepsilonϕ$ at each point.
