On the Whitney Extension-Interpolation-Alignment problem for almost isometries with small distortion in $\Bbb R^D$

arXiv1411.2468MaRDI QIDQ6507435

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Abstract: In this paper, we study the following problem. Let $Dgeq2$, $Ssubsetmathbb{R}^D$ be finite and let $phi:Somathbb{R}^D$ with $phi$ a small distortion on $S$. We solve the Whitney extension-interpolation-alignment problem of how to understand when $phi$ can be extended to a function $Phi:mathbb{R}^{D}omathbb{R}^D$ which is a smooth small distortion on $mathbb{R}^D$.

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