Sobolev estimates in parabolic geometries
Bent Ørsted, Aarhus Universitet, Aarhus, Denmark
Abstract
In spectral geometry a key role is played by various forms
of Sobolev inequalities, and some of these lead to estimates with
applications in other parts of mathematics, for example the logarithmic
Sobolev inequality. In this talk we shall discuss replacing Riemannian
geometry by for example CR geometry, the natural geometry on the
boundary of domains in complex manifolds, and prove generalizations
of the logarithmic Sobolev inequality to this setting.