Differential and Integral Equations

Minimal disc-type surfaces embedded in a perturbed cylinder

Mouhamed Moustapha Fall and Carlo Mercuri

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Abstract

In the present note, we deal with small perturbations of an infinite cylinder in three-dimensional Euclidian space. We find minimal disc-type surfaces embedded in the cylinder and intersecting its boundary perpendicularly. The existence and localization of those minimal discs is a consequence of a non-degeneracy condition for the critical points of a functional related to the oscillations of the cylinder from the flat configuration.

Article information

Source
Differential Integral Equations Volume 22, Number 11/12 (2009), 1115-1124.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019407

Mathematical Reviews number (MathSciNet)
MR2555639

Zentralblatt MATH identifier
1240.53004

Subjects
Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 35B20: Perturbations

Citation

Fall, Mouhamed Moustapha; Mercuri, Carlo. Minimal disc-type surfaces embedded in a perturbed cylinder. Differential Integral Equations 22 (2009), no. 11/12, 1115--1124. https://projecteuclid.org/euclid.die/1356019407.


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