Mathematical Research Letters

Volume 13, Issue 6, November 2006 pp. 833-845.

Examples concerning Whitney's $C^m$ extension problem

Authors: Edward Bierstone (1), Charles Fefferman (2), Pierre D. Milman (3), and Wieslaw Pawlucki (4)
Author institution: University of Toronto (1), Princeton University (2), University of Toronto (3), and Uniwersytet Jagiellonski (4)

Summary: We present several examples connected with our articles on Whitney's extension problem. The first shows that Glaeser iterations cannot be avoided in the $C^m$ extension criterion of \cite{F2}, and the remaining three are counterexamples to $C^m$ extension assuming a weaker criterion that was used to prove a $C^\infty$ extension theorem for closed subanalytic sets, in \cite{BMP1}.

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