Revista Matemática Iberoamericana

A Generalized Sharp Whitney Theorem for Jets

Charles Fefferman

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Abstract

Suppose that, for each point $x$ in a given subset $E \subset \mathbb{R}^n$, we are given an $m$-jet $f(x)$ and a convex, symmetric set $\sigma(x)$ of $m$-jets at $x$. We ask whether there exist a function $F \in C^{m , \omega} ( \mathbb{R}^n )$ and a finite constant $M$, such that the $m$-jet of $F$ at $x$ belongs to $f ( x ) + M \sigma ( x )$ for all $x \in E$. We give a necessary and sufficient condition for the existence of such $F , M$, provided each $\sigma(x)$ satisfies a condition that we call ``Whitney $\omega$-convexity''.

Article information

Source
Rev. Mat. Iberoamericana, Volume 21, Number 2 (2005), 577-688.

Dates
First available in Project Euclid: 11 August 2005

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1123766807

Mathematical Reviews number (MathSciNet)
MR2174917

Zentralblatt MATH identifier
1102.58004

Subjects
Primary: 49K24 52A35: Helly-type theorems and geometric transversal theory

Keywords
extension problems Whitney convexity Whitney $\omega$-convexity

Citation

Fefferman, Charles. A Generalized Sharp Whitney Theorem for Jets. Rev. Mat. Iberoamericana 21 (2005), no. 2, 577--688. https://projecteuclid.org/euclid.rmi/1123766807


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