A1 Journal article (refereed)
Extending an example by Colding and Minicozzi (2020)

Ruffoni, L., & Tripaldi, F. (2020). Extending an example by Colding and Minicozzi. Journal of Geometric Analysis, 30(1), 1028-1041. https://doi.org/10.1007/s12220-019-00177-4

JYU authors or editors

Tripaldi, Francesca

Publication details

All authors or editors: Ruffoni, Lorenzo; Tripaldi, Francesca

Journal or series: Journal of Geometric Analysis

ISSN: 1050-6926

eISSN: 1559-002X

Publication year: 2020

Volume: 30

Issue number: 1

Pages range: 1028-1041

Publisher: Springer

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1007/s12220-019-00177-4

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/66909

Web address of parallel published publication (pre-print): https://arxiv.org/abs/1810.00359

Web address where publication is available: https://arxiv.org/abs/1810.00359

Abstract

Extending an example by Colding and Minicozzi (Trans Am Math Soc 356(1):283–289, 2003), we construct a sequence of properly embedded minimal disks \Sigma _i in an infinite Euclidean cylinder around the x_3-axis with curvature blow-up at a single point. The sequence converges to a non-smooth and non-proper minimal lamination in the cylinder. Moreover, we show that the disks \Sigma _i are not properly embedded in a sequence of open subsets of \mathbb {R}^3 that exhausts \mathbb {R}^3.

Keywords: differential geometry; calculus of variations

Free keywords: minimal surfaces; minimal laminations; Colding-Minicozzi theory

Fields of science: