Geometry, Topology and Dynamics Seminar
Kai Rajala
University of Jyvaskyla
Quantitative isoperimetric inequalities and quasiconformal maps
Abstract: The so-called Bonnesen-style inequalities show that planar Jordan domains that
are almost minimizers of the isoperimetric problem are geometrically almost
disks, with quantitative bounds. By considering cusp domains, one sees that such
inequalities do not hold in higher dimensions. We show, using the results of
Hall and Fusco, Maggi, and Pratelli, that there exists a Bonnesen-style inequality
in every dimension for images of the unit ball under global quasiconformal maps
and more general homeomorphisms with controlled geometry.
Wednesday April 1, 2009 at 3:00 PM in SEO 612