## Journal of Differential Geometry

### One-sided complete stable minimal surfaces

Antonio Ros

#### 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

#### 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