Least area planes in hyperbolic $3$-space are properly embedded Baris Coskunuzer 53A1057M50asymptotic plateau problemproperly embeddedleast area plane We show that if $\Sigma$ is an embedded least area (area minimizing) plane in $\mathbb{H}^3$ whose asymptotic boundary is a simple closed curve with at least one smooth point, then $\Sigma$ is properly embedded in $\mathbb{H}^3$. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3447 10.1512/iumj.2009.58.3447 en Indiana Univ. Math. J. 58 (2009) 381 - 392 state-of-the-art mathematics http://iumj.org/access/