12/8/2006

Bruce Kleiner
Yale University

BiLipschitz embedding in Banach spaces

Motivated by a conjecture from computer science, I will discuss biLipschitz embeddings X ---> V where X is a metric space and V is a Banach space. The focus will be on the case when X is a metric measure space satisfying a Poincare inequality. Of particular interest is the case when the target Banach space is L^1, in which case there is a new link between embedding questions and the structure of sets of finite perimeter in X. By exploiting recent work on geometric measure theory in the Heisenberg group, we show that the Heisenberg group cannot be biLipschitz embedded in L^1, confirming a conjecture of Assaf Naor. This is joint work with Jeff Cheeger.