Matthias Aschenbrenner : Lipschitz maps and definability.

Posted by , part of the Logic Seminar.

At

Sept. 22, 2009, 4 p.m.

In

SEO 612

Abstract

A classical result due to Kirszbraun (1934), which plays an important role in geometric measure theory, shows that every Lipschitz map $S\to\mathbb R^n$ on a subset $S$ of $\mathbb R^m$ can be extended to a Lipschitz map $\mathbb R^m\to\mathbb R^n$ with the same Lipschitz constant. The usual proofs of this theorem in the literature employ, in some form or other, the Axiom of Choice. We discuss a definable version of this result. (Joint with Andreas Fischer.)

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