WHITNEY PROBLEMS.

Whitney problems originate from Hassler Whitney seminal papers of 1934, they deal with the following questions: given a function f on an arbitrary subset of a Euclidean space, how can one tell if this functions is extendible to a function of a prescribed smoothness on the whole Euclidean space?

Whitney was able to develop very important techniques which allowed him to answer the question above in the case of the one-dimensional space and the space of m times continuously differentiable functions on this space. He also answered similar questions in any dimension if you are given not just the function f but actually a string of functions which are supposed to be the related derivatives of f.

He also was able to give a simple geometric sufficient condition for an open bounded domain in the Euclidean space to be an extension domain, meaning that for every m any function on the domain with bounded partial derivatives of orders less or equal to m, can be extended to an m times differentiable function on the whole Euclidean space.

Recently Charles Fefferman was able to answer the original question of Whitney in full generality. This led to a number of very important developments in the field.

A WHITNEY PROBLEMS WORKSHOP was held at the College of William and Mary on August 11-17, 2008. It was organized by Charles Fefferman (Princeton University) and me.

The Workshop was generously supported by a grant from the Office of Naval Research, by the Office of Vice Provost of the College of William and Mary, and by the Mathematics Departments of the College of William and Mary and of the Princeton University.

WHITNEY PROBLEMS WORKSHOP 2008:

1. Schedule of talks and abstracts whitney\whitneyschedule (1).pdf

2. List of open problems whitney\whitproblems.pdf.

3. Comments to the list (continuously updated):

(a) Arie Israel: whitney\YossiCounterexample.pdf, whitney\CharlieProblemModification2.pdf

4. Link to video files of all lectures of the workshop http://whitneyworkshop2008.blip.tv.

5. Photos.

FUTURE WHITNEY WORKSHOPS

We plan to have two more Whitney Problems Workshops in 2009 and 2010.  We shall post information about these Workshops on this site. If you are interested in participating in these Workshops, please contact Charles Fefferman cf@math.princeton.edu or me nxzobi@wm.edu.