PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Nigel Higson, Mari Royer.

Title:Sharp Gagliardo--Nirenberg--Sobolev inequalities and conformal geometry
Seminar:Department of Mathematics Colloquium
Speaker:Jeffrey Case, Princeton University
Abstract:
There is a deep connection between curvature prescription problems in conformal geometry and sharp Sobolev inequalities. One famous example is the connection between prescribing conformal metrics with constant scalar curvature and the sharp $L^2$ Sobolev inequalty. Another example is the connection between prescribing Perelman's weighted scalar curvature and the sharp logarithmic Sobolev inequality. In this talk, I will describe an interpolating family of curvature prescription problems on smooth metric measure spaces which connect the scalar curvature to Perelman's weighted scalar curvature and are related to the family of sharp Gagliardo-Nirenberg-Sobolev inequalities discovered by Del Pino and Dolbeault. In particular, this provides a new perspective on Perelman's $W$-functional and suggests an approach to finding higher order analogues.

Room Reservation Information

Room Number:MB114
Date:02 / 20 / 2014
Time:03:35pm - 04:25pm