Geometry & Topology

Approximation theory for nonorientable minimal surfaces and applications

Antonio Alarcón and Francisco J López

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Abstract

We prove a version of the classical Runge and Mergelyan uniform approximation theorems for nonorientable minimal surfaces in Euclidean 3–space 3. Then we obtain some geometric applications. Among them, we emphasize the following ones:

  • A Gunning–Narasimhan-type theorem for nonorientable conformal surfaces.
  • An existence theorem for nonorientable minimal surfaces in 3 with arbitrary conformal structure, properly projecting into a plane.
  • An existence result for nonorientable minimal surfaces in 3 with arbitrary conformal structure and Gauss map omitting one projective direction.

Article information

Source
Geom. Topol., Volume 19, Number 2 (2015), 1015-1062.

Dates
Received: 2 October 2013
Revised: 29 May 2014
Accepted: 6 July 2014
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1510858718

Digital Object Identifier
doi:10.2140/gt.2015.19.1015

Mathematical Reviews number (MathSciNet)
MR3336277

Zentralblatt MATH identifier
1314.49026

Subjects
Primary: 49Q05: Minimal surfaces [See also 53A10, 58E12]
Secondary: 30E10: Approximation in the complex domain

Keywords
nonorientable minimal surfaces uniform approximation

Citation

Alarcón, Antonio; López, Francisco J. Approximation theory for nonorientable minimal surfaces and applications. Geom. Topol. 19 (2015), no. 2, 1015--1062. doi:10.2140/gt.2015.19.1015. https://projecteuclid.org/euclid.gt/1510858718


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