Mathematical Research Letters

Volume 13 (2006)

Number 6

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

Pages: 833 – 845



Edward Bierstone (University of Toronto)

Charles Fefferman (Princeton University)

Pierre D. Milman (University of Toronto)

Wieslaw Pawlucki (Uniwersytet Jagiellonski)


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}.

Published 1 January 2006