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A Nash–Kuiper theorem for $C^{1,\frac{1}{5}-\delta}$ immersions of surfaces in 3 dimensions


De Lellis, Camillo; Inauen, Dominik; Székelyhidi Jr., László (2018). A Nash–Kuiper theorem for $C^{1,\frac{1}{5}-\delta}$ immersions of surfaces in 3 dimensions. Revista matemática iberoamericana, 34(3):1119-1152.

Abstract

We prove that, given a $C^2$ Riemannian metric $g$ on the 2-dimensional disk $D_2$, any short $C^1$ immersion of $(D_2,g)$ into $\mathbb{R}^3$ can be uniformly approximated with $C^{1,α}$ isometric immersions for any $α<\frac{1}{5}$. This statement improves previous results by Yu. F. Borisov and of a joint paper of the first and third author with S. Conti.

Abstract

We prove that, given a $C^2$ Riemannian metric $g$ on the 2-dimensional disk $D_2$, any short $C^1$ immersion of $(D_2,g)$ into $\mathbb{R}^3$ can be uniformly approximated with $C^{1,α}$ isometric immersions for any $α<\frac{1}{5}$. This statement improves previous results by Yu. F. Borisov and of a joint paper of the first and third author with S. Conti.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:General Mathematics
Language:English
Date:27 August 2018
Deposited On:17 Jan 2019 10:46
Last Modified:25 Sep 2019 00:01
Publisher:Universidad de La Rioja ; Dialnet
ISSN:0213-2230
OA Status:Green
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.4171/rmi/1019

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