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De Lellis, Camillo; Inauen, Dominik (2020). C1,α isometric embeddings of polar caps. Advances in Mathematics, 363:106996.
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.
| 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: | 08 Sep 2024 03:31 |
| 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 |
De Lellis, Camillo