Journal of Differential Geometry

Stable minimal surfaces in M × ℝ

William H. Meeks III


In this paper, we classify the stable properly embedded orientable minimal surfaces in M × ℝ, where M is a closed orientable Riemannian surface. We show that such a surface is a product of a stable embedded geodesic on M with ℝ, a minimal graph over a region of M bounded by stable geodesics, M × {t} for some t ∈ ℝ, or is in a moduli space of periodic multigraphs parametrized by P × ℝ+, where P is the set of primitive (non-multiple) homology classes in H1(M).

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J. Differential Geom., Volume 68, Number 3 (2004), 515-534.

First available in Project Euclid: 9 May 2005

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Meeks III, William H. Stable minimal surfaces in M × ℝ. J. Differential Geom. 68 (2004), no. 3, 515--534. doi:10.4310/jdg/1115669593.

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