Header

UZH-Logo

Maintenance Infos

C1,α isometric embeddings of polar caps


De Lellis, Camillo; Inauen, Dominik (2020). C1,α isometric embeddings of polar caps. Advances in Mathematics, 363:106996.

Abstract

We study isometric embeddings of C2 Riemannian manifolds in the Euclidean space and we establish that the Hölder space C1,12is critical in a suitable sense: in particular we prove that for α >12 the Levi-Civita connection of any isometric immersion is induced by the Euclidean connection, whereas for any α <12 we construct C1,α isometric embeddings of portions of the standard 2-dimensional sphere for which such property fails.

Abstract

We study isometric embeddings of C2 Riemannian manifolds in the Euclidean space and we establish that the Hölder space C1,12is critical in a suitable sense: in particular we prove that for α >12 the Levi-Civita connection of any isometric immersion is induced by the Euclidean connection, whereas for any α <12 we construct C1,α isometric embeddings of portions of the standard 2-dimensional sphere for which such property fails.

Statistics

Citations

Dimensions.ai Metrics
1 citation in Web of Science®
1 citation in Scopus®
Google Scholar™

Altmetrics

Downloads

0 downloads since deposited on 01 Oct 2020
0 downloads since 12 months

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:340 Law
610 Medicine & health
510 Mathematics
Scopus Subject Areas:Physical Sciences > General Mathematics
Uncontrolled Keywords:General Mathematics
Language:English
Date:1 March 2020
Deposited On:01 Oct 2020 10:20
Last Modified:02 Oct 2020 20:00
Publisher:Elsevier
ISSN:0001-8708
OA Status:Closed
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1016/j.aim.2020.106996

Download

Closed Access: Download allowed only for UZH members

Content: Published Version
Language: English
Filetype: PDF - Registered users only
Size: 597kB
View at publisher