Journal of Differential Geometry

Stable minimal surfaces in M × ℝ

William H. Meeks III

Abstract

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).

Article information

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

Dates
First available in Project Euclid: 9 May 2005

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1115669593

Digital Object Identifier
doi:10.4310/jdg/1115669593

Mathematical Reviews number (MathSciNet)
MR2144539

Zentralblatt MATH identifier
1079.53089

Citation

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


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