Introduction to metric and comparison geometry

Geometry Topology Working Seminar
Friday, February 27, 2009 - 3:05pm
2.5 hours
Skiles 269
Ga Tech
Comparison geometry studies Riemannian manifolds with a given curvature bound. This minicourse is an introduction to volume comparison (as developed by Bishop and Gromov), which is fundamental in understanding manifolds with a lower bound on Ricci curvature. Prerequisites are very modest: we only need basics of Riemannian geometry, and fluency with fundamental groups and metric spaces. In the third (2 hour) lecture I shall prove volume and Laplacian comparison theorems.