Stable embedded minimal surfaces bounded by a straight line

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Abstract

We prove that if \({M\subset \mathbb{R}^3}\) is a properly embedded oriented stable minimal surface whose boundary is a straight line and the area of M in extrinsic balls grows quadratically in the radius, then M is a half-plane or half of the classical Enneper minimal surface. This solves a conjecture posed by B. White in Geometric Analysis and the Calculus of Variations for Stefan Hildebrandt, International Press, Somerville, 1996.

Mathematics Subject Classification (1991)

Primary: 53A10 Secondary: 49Q05 Secondary: 53C42 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of Geometry and TopologyUniversity of GranadaGranadaSpain

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