\(C^{1,1-\varepsilon}\) isometric embeddings (Q6571607)
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scientific article; zbMATH DE number 7880403
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(C^{1,1-\varepsilon}\) isometric embeddings |
scientific article; zbMATH DE number 7880403 |
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\(C^{1,1-\varepsilon}\) isometric embeddings (English)
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12 July 2024
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This paper is devoted to the construction of isometric emebeddings of \(n\)-dimensional manifolds in codimension \(1+n(n+1)/2\). The techniques of convex integration as well as ideas of \textit{A. Källen} [Ark. Mat. 16, 29--50 (1978; Zbl 0381.35014)] and \textit{H. Kröner} [``Irregular Isometric Embeddings of Compact Manifolds'', Master Thesis Mathematics, Institute for Applied Mathematics (2012)] are used to improve results on the regularity of these isometric embeddings.
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isometric embeddings
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local \(h\)-principle
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Nash-Kuiper theorem
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convex integration
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