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The half space property for cmc 1/2 graphs in \(\mathbb {E}(-1,\tau )\)

  • Laurent MazetEmail author
Article

Abstract

In this paper, we prove a half-space theorem with respect to constant mean curvature 1/2 entire graphs in \(\mathbb {E}(-1,\tau )\). If \(\Sigma \) is such an entire graph and \(\Sigma '\) is a properly immersed constant mean curvature 1/2 surface included in the mean convex side of \(\Sigma \) then \(\Sigma '\) is a vertical translate of \(\Sigma \). We also have an equivalent statement for the non mean convex side of \(\Sigma \).

Mathematics Subject Classification

53A10 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Laboratoire d’Analyse et Mathématiques Appliquées, CNRS UMR8050, UFR des Sciences et TechnologieUniversité Paris-EstCréteil CedexFrance

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