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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
41/2003

On the Sobolev space of isometric immersions

Mohammed Reza Pakzad

Abstract

We prove that every $W^{2,2}$ isometric immersion from a convex regular domain of ${\mathbb R}^2$ into ${\mathbb R}^3$ can be approximated in $W^{2,2}$-norm by smooth isometric immersions from the same domain into ${\mathbb R}^3$.

Received:
30.04.03
Published:
30.04.03
MSC Codes:
46T99, 53A05, 53C24, 58Dxx, 74Kxx
Keywords:
rigidity of isometric immersions, developable surfaces, thin elastic bodies, curvature functionals, sobolev spaces of mappings

Related publications

inJournal
2004 Repository Open Access
Mohammad Reza Pakzad

On the Sobolev space of isometric immersions

In: Journal of differential geometry, 66 (2004) 1, pp. 47-69