Stable embedded minimal surfaces bounded by a straight line

Pérez, Joaquín
June 2007
Calculus of Variations & Partial Differential Equations;Jun2007, Vol. 29 Issue 2, p267
Academic Journal
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.


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