Calculus of Variations and Partial Differential Equations

, Volume 29, Issue 2, pp 267–279

Stable embedded minimal surfaces bounded by a straight line

Original Article

DOI: 10.1007/s00526-006-0069-2

Cite this article as:
Pérez, J. Calc. Var. (2007) 29: 267. doi:10.1007/s00526-006-0069-2
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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: 53A10Secondary: 49Q05Secondary: 53C42

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of Geometry and TopologyUniversity of GranadaGranadaSpain