Special Colloquium
Leonid V. Kovalev
Texas A&M University
Monotonicity in geometric mapping theory and functional analysis
Abstract: The defining property of increasing functions,
(f(a)-f(b))*(a-b)>0, can be extended to mappings in Hilbert spaces and in
more general Banach spaces. Although the studies of such mappings have
been traditionally driven by the PDE theory, I am more interested in their
geometric properties. Monotone mappings have been used to (1) improve the
results of Bonk, Heinonen, and Saksman (2004) on the singular sets of
quasiconformal maps; (2) prove the conjecture of Tyson (1999) on the
conformal dimension of metric spaces; (3) construct quasiconformal maps as
vector-valued potentials of doubling measures. This talk is partly based
on joint research with Diego Maldonado and Jang-Mei Wu.
There will be a meet and greet right after the talk in SEO 300. Coffee, tea, & cookies will be provided.
Wednesday January 16, 2008 at 3:00 PM in SEO 636