Can I read Slab Theorem and Halfspace Theorem for constant mean curvature surfaces in $\mathbb H^2\times\mathbb R$ on EtoBox?

Slab Theorem and Halfspace Theorem for constant mean curvature surfaces in $\mathbb H^2\times\mathbb R$ by Hauswirth, Laurent; Menezes, Ana; Rodriguez, Magdalena is a scholarly article available to read on EtoBox.

What is Slab Theorem and Halfspace Theorem for constant mean curvature surfaces in $\mathbb H^2\times\mathbb R$ about?

We prove that a properly embedded annular end of a surface in $\mathbb H^2\times\mathbb R$ with constant mean curvature $0<H\leq \frac{1}{2}$ can not be contained in any horizontal slab. Moreover, we show that a properly embedded surface with constant mean curvature $0<H\leq \frac{1}{2}$ contained in $\mathbb H^2\times[0,+\infty)$ and with finite topology is necessarily a graph over a simply connected domain of $\mathbb H^2$. For the case $H=\frac{1}{2}$, the graph is entire.

Author

Hauswirth, Laurent; Menezes, Ana; Rodriguez, Magdalena

Published

2021

Language

EN