IUMJ

Title: Maximum principles at infinity for surfaces of bounded mean curvature in $\mathbb{R}^3$ and $\mathbb{H}^3$

Authors: Ronaldo F. de Lima and William Meeks III

Issue: Volume 53 (2004), Issue 5, 1211-1224

Abstract:

Let $M_1$, $M_2$ be disjoint surfaces in $\mathbb{R}^3$ or $\mathbb{H}^3$ with (possibly empty) boundaries $\partial M_1$, $\partial M_2$ and bounded mean curvature. We establish a maximum principle at infinity for these surfaces by proving that under certain conditions on their curvatures, $M_1$ and $M_2$ cannot approach each other asymptotically.