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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:
Apr 30, 2003
Published:
Apr 30, 2003
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