Tel-Aviv University
School of Mathematical Sciences

Department Colloquium

Monday, December 13, 2010

Schreiber 006, 12:15

Pavel Shvartsman

Technion, Israel Institute of Technology

The Whitney problem: how to measure
smoothness of functions on finite sets

Abstract: In 1934 H. Whitney posed the following problem: Let f be a function defined on a closed subset E of R^n. How can we tell whether f extends to a C^m-smooth function defined on all of R^n? We discuss different aspects of this classical problem including its interesting connections with Convex Geometry (Helly's theorem), Lipschitz selections of set-valued functions and Analysis on Riemannian manifolds. The main part of the talk will address the "finiteness principle" which states that the Whitney extension problem can be reduced to the same kind of the problem, but for finite sets with prescribed number of points. We will present several constructive criteria for restrictions of C^2-functions and Sobolev W^1_p and W^2_p-functions to arbitrary closed subsets of R^2.

No special background is necessary.

Coffee will be served at 12:00 before the lecture
at Schreiber building 006