, Volume 13, Issue 2, pp 101-116

Maximum principle at infinity for complete minimal surfaces in flat 3-manifolds

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Abstract

The main result of this paper is the following maximum principle at infinity:Theorem.Let M 1 and M 2 be two disjoint properly embedded complete minimal surfaces with nonempty boundaries, that are stable in a complete flat 3-manifold. Then dist(M 1,M 2)=min(dist(∂M 1,M 2), dist(∂M 2,M 1)).In case one boundary is empty, e.g. M 1,then dist(M 1,M 2)=dist(∂M 2,M 1).If both boundaries are empty, then M 1 and M 2 are flat.