We study isometric embeddings of C-2 Riemannian manifolds in the Euclidean space and we establish that the Holder space C-1,C-1/2 is critical in a suitable sense: in particular we prove that for alpha > 1/2 the Levi-Civita connection of any isometric immersion is induced by the Euclidean connection, whereas for any alpha < 1/2 we construct Cr-1,Cr-alpha isometric embeddings of portions of the standard 2-dimensional sphere for which such property fails. (C) 2020 Elsevier Inc. All rights reserved
C1,α isometric embeddings of polar caps
De Lellis, C.;
2020-01-01
Abstract
We study isometric embeddings of C-2 Riemannian manifolds in the Euclidean space and we establish that the Holder space C-1,C-1/2 is critical in a suitable sense: in particular we prove that for alpha > 1/2 the Levi-Civita connection of any isometric immersion is induced by the Euclidean connection, whereas for any alpha < 1/2 we construct Cr-1,Cr-alpha isometric embeddings of portions of the standard 2-dimensional sphere for which such property fails. (C) 2020 Elsevier Inc. All rights reservedFile in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
2020_AdvMath_363_106996_DeLellis.pdf
non disponibili
Tipologia:
Versione Editoriale (PDF)
Licenza:
Non pubblico
Dimensione
660.21 kB
Formato
Adobe PDF
|
660.21 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
