MINIMAL PLANES IN ASYMPTOTICALLY FLAT THREE-MANIFOLDS

In this paper, we improve a result by Chodosh and Ketover [2]. We prove that, in an asymptotically flat 3-manifold M that contains no closed minimal surfaces, fixing q is an element of M and V a 2-plane in TqM there is a properly embedded minimal plane Sigma in M such that q is an element of Sigma and T-q Sigma = V. We also prove that fixing three points in M there is a properly embedded minimal plane passing through these three points.