Introduction to metric and comparison geometry

Geometry Topology Working Seminar
Friday, February 20, 2009 - 15:00
2 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. The second (2 hour) lecture is about Gromov-Hausdorff convergence, which provides a natural framework to studying degenerations of Riemannian metrics.