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Whitney's Problem on Extendability of Functions and an Intrinsic Metric

✍ Scribed by Nahum Zobin

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
483 KB
Volume
133
Category
Article
ISSN
0001-8708

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✦ Synopsis

We consider the space of functions with bounded (k+1) th derivatives in a general domain in R n . Is every such function extendible to a function of the same class defined on the whole R n ? H. Whitney showed that the equivalence of the intrinsic ( =geodesic) metric in this domain to the Euclidean one is sufficient for such extendability. There was an old conjecture (going back to H. Whitney) that this equivalence is also necessary for extendability. We disprove this conjecture and construct examples of domains in R 2 such that the above extendability holds but the analogous property for smaller k fails. Our study is based on a duality approach. 1998 Academic Press

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