Annals of Global Analysis and Geometry

, Volume 13, Issue 2, pp 101–116

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

  • Marc Soret

DOI: 10.1007/BF01120326

Cite this article as:
Soret, M. Ann Glob Anal Geom (1995) 13: 101. doi:10.1007/BF01120326


The main result of this paper is the following maximum principle at infinity:Theorem.Let M1and M2be two disjoint properly embedded complete minimal surfaces with nonempty boundaries, that are stable in a complete flat 3-manifold. Then dist(M1,M2)=min(dist(∂M1,M2), dist(∂M2,M1)).In case one boundary is empty, e.g. M1,then dist(M1,M2)=dist(∂M2,M1).If both boundaries are empty, then M1and M2are flat.

Key words

Maximum principle Minimal surfaces 

MSC 1991

53 A 10 

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Marc Soret
    • 1
  1. 1.Département de MathématiquesUniversité F. RabelaisToursFrance

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