From January 15th to January 30th, I will have the great pleasure to visit the TIFR Centre For Applicable Mathematics in Bangalore, India. I will be lecturing on some aspects of geometric inequalities on sub-Riemannian manifolds.

Here is a preliminary version of the lecture notes: Bangalore.

The four lectures will mainly be divided into three parts:

1. Sub-Laplacian comparison theorems
2. Volume doubling properties and Poincare inequalities on sub-Riemannian manifolds
3. Isoperimetric and Sobolev inequalities

A main theme in those topics is the use of a generalized curvature dimension condition which is valid for a large class of  hypoelliptic second-order differential operators.