Extending an example by Colding and Minicozzi

Ruffoni, Lorenzo; Tripaldi, Francesca (2020). Extending an example by Colding and Minicozzi. Journal of geometric analysis, 30(1), pp. 1028-1041. Springer-Verlag 10.1007/s12220-019-00177-4

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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 R^3 that exhausts R^3.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Tripaldi, Francesca

Subjects:

500 Science > 510 Mathematics

ISSN:

1050-6926

Publisher:

Springer-Verlag

Funders:

[UNSPECIFIED] Academy of Finland ; [UNSPECIFIED] University of Jyväskylä ; [18] European Research Council ; [UNSPECIFIED] Marie Skłodowska-Curie Grant

Language:

English

Submitter:

Sebastiano Don

Date Deposited:

27 Jan 2021 17:08

Last Modified:

11 Mar 2021 20:33

Publisher DOI:

10.1007/s12220-019-00177-4

ArXiv ID:

1810.00359

Uncontrolled Keywords:

Minimal surfaces, Minimal laminations, Colding–Minicozzi theory

BORIS DOI:

10.48350/151280

URI:

https://boris.unibe.ch/id/eprint/151280

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