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\title {WHITNEY'S PROBLEM ON EXTENDABILITY OF FUNCTIONS AND AN INTRINSIC
METRIC}
\author{Nahum Zobin, Department of Mathematics,
Ohio State University, Columbus OH 43220,
email: \tt{zobin@math.ohio-state.edu}}
\markboth{Santa Barbara Symposium -- N.~Zobin}
{Santa Barbara Symposium -- N.~Zobin}
\begin{document}\label{l-conf-nz}
\maketitle
Whitney's Problem deals with the geometric
conditions of extendability of smooth functions defined in a bounded
connected domain in Euclidean space. The long-standing conjecture
(going back to Whitney, 1934) was that the equivalence of the natural
geodesic metric on a domain to the Euclidean metric is necessary for the
extendability of functions with bounded higher derivatives (the
sufficiency was proved by Whitney). We disprove the conjecture for all
dimensions starting from 2, and verify it for planar finitely connected
domains. The results are published in the papers listed below.
\begin{thebibliography}{3}
\bibitem {1} N.~Zobin, {\em Whitney's problem: extendability of
functions and intrinsic metric},
C.R. Acad. Sci. Paris, S\'erie 1, {\bf 320} (1995), 781-786.
\bibitem{2} N.~Zobin,
{\em Whitney's problem on extendability of functions and an intrinsic
metric},
Adv. in Math. {\bf 133} (1998), 96 -- 132.
\bibitem{3} N.~Zobin, {\em Extension of
smooth functions from finitely connected planar domains}, Journal of Geom.
Analysis, to appear.
\end{thebibliography}
\end{document}