Open Access
Nov 2004 Stable minimal surfaces in M × ℝ
William H. Meeks III
J. Differential Geom. 68(3): 515-534 (Nov 2004). DOI: 10.4310/jdg/1115669593


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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William H. Meeks III. "Stable minimal surfaces in M × ℝ." J. Differential Geom. 68 (3) 515 - 534, Nov 2004.


Published: Nov 2004
First available in Project Euclid: 9 May 2005

zbMATH: 1079.53089
MathSciNet: MR2144539
Digital Object Identifier: 10.4310/jdg/1115669593

Rights: Copyright © 2004 Lehigh University

Vol.68 • No. 3 • Nov 2004
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