Maximum principles at infinity for surfaces of bounded mean curvature in $\mathbb{R}^3$ and $\mathbb{H}^3$ Ronaldo de LimaWilliam Meeks III 53A1053A35constant mean curvaturemaximum principle 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. Indiana University Mathematics Journal 2004 text pdf 10.1512/iumj.2004.53.2531 10.1512/iumj.2004.53.2531 en Indiana Univ. Math. J. 53 (2004) 1211 - 1224 state-of-the-art mathematics http://iumj.org/access/