Journal of Differential Geometry

One-sided complete stable minimal surfaces

Antonio Ros

Full-text: Open access

Abstract

We prove that there are no complete one-sided stable minimal surfaces in the Euclidean 3-space. We classify least area surfaces in the quotient of $\mathbb{R}^3$ by one or two linearly independent translations and we give sharp upper bounds of the genus of compact two-sided index one minimal surfaces in non-negatively curved ambient spaces. Finally we estimate from below the index of complete minimal surfaces in flat spaces in terms of the topology of the surface

Article information

Source
J. Differential Geom., Volume 74, Number 1 (2006), 69-92.

Dates
First available in Project Euclid: 30 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1175266182

Digital Object Identifier
doi:10.4310/jdg/1175266182

Mathematical Reviews number (MathSciNet)
MR2260928

Zentralblatt MATH identifier
1110.53009

Subjects
Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]

Citation

Ros, Antonio. One-sided complete stable minimal surfaces. J. Differential Geom. 74 (2006), no. 1, 69--92. doi:10.4310/jdg/1175266182. https://projecteuclid.org/euclid.jdg/1175266182


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