Distortion of spheres and surfaces in space

Baader, Sebastian; Studer, Luca; Züst, Roger (2020). Distortion of spheres and surfaces in space. The quarterly journal of mathematics, 71(3), pp. 981-988. Oxford University Press 10.1093/qmathj/haaa011

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It is known that the surface of a cone over the unit disc with large height has smaller distortion than the standard embedding of the 2-sphere in R3⁠. In this note we show that distortion minimizers exist among convex embedded 2-spheres and have uniformly bounded eccentricity. Moreover, we prove that π/2 is a sharp lower bound on the distortion of embedded closed surfaces of positive genus.

Item Type:

Journal Article (Original Article)

Division/Institute:

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

UniBE Contributor:

Baader, Sebastian; Studer, Luca and Züst, Roger

Subjects:

500 Science > 510 Mathematics

ISSN:

0033-5606

Publisher:

Oxford University Press

Language:

English

Submitter:

Sebastiano Don

Date Deposited:

27 Jan 2021 16:37

Last Modified:

11 Mar 2021 20:01

Publisher DOI:

10.1093/qmathj/haaa011

ArXiv ID:

1904.07824

BORIS DOI:

10.48350/151218

URI:

https://boris.unibe.ch/id/eprint/151218

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