On the Whitney Extension-Interpolation-Alignment problem for almost isometries with small distortion in $\Bbb R^D$
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arXiv
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| Format: | Preprint |
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2014
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| _version_ | 1866914690024603648 |
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| author | Damelin, S. B Fefferman, C. |
| author_facet | Damelin, S. B Fefferman, C. |
| contents | In this paper, we study the following problem. Let $D\geq 2$, $S\subset \mathbb R^D$ be finite and let $ϕ:S\to \mathbb R^D$ with $ϕ$ a small distortion on $S$. We solve the Whitney extension-interpolation-alignment problem of how to understand when $ϕ$ can be extended to a function $Φ:\mathbb R^D\to \mathbb R^D$ which is a smooth small distortion on $\mathbb R^D$. The work in this paper appears in the research memoir [14] |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1411_2468 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | On the Whitney Extension-Interpolation-Alignment problem for almost isometries with small distortion in $\Bbb R^D$ Damelin, S. B Fefferman, C. Metric Geometry 58C25, 42B35, 94A08, 94C30, 41A05, 68Q25, 30E05, 26E10, 68Q17 In this paper, we study the following problem. Let $D\geq 2$, $S\subset \mathbb R^D$ be finite and let $ϕ:S\to \mathbb R^D$ with $ϕ$ a small distortion on $S$. We solve the Whitney extension-interpolation-alignment problem of how to understand when $ϕ$ can be extended to a function $Φ:\mathbb R^D\to \mathbb R^D$ which is a smooth small distortion on $\mathbb R^D$. The work in this paper appears in the research memoir [14] |
| title | On the Whitney Extension-Interpolation-Alignment problem for almost isometries with small distortion in $\Bbb R^D$ |
| topic | Metric Geometry 58C25, 42B35, 94A08, 94C30, 41A05, 68Q25, 30E05, 26E10, 68Q17 |
| url | https://arxiv.org/abs/1411.2468 |