MATH 86100: Metric Geometry

CUNY Graduate Center Fall 2005

Thursdays 11:45-1:45 pm

Room 5417

Professor: Christina Sormani

Topics: Lipschitz Maps, Hausdorff Measure and Dimension, Length Spaces, Hyperbolic Space, Alexandrov Spaces, Fundamental Groups of these Spaces, Gromov-Hausdorff Convergence, Gromov's Compactness Theorem, Quasi Isometries, Gromov Hyperbolic Spaces, Gromov-Hausdorff Limits, Tangent Cones at Infinity, and Metric Measure Spaces. Applications to Riemannian Geometry, the work of Perelman and Complex Analysis will be discussed.

Text: Burago-Burago-Ivanov's "A Course in Metric Geometry" AMS Graduate Studies in Mathematics Volume 33. See this link for typos. It's easiest to order this book from the AMS.

Prerequisites: Graduate Topology and Real Analysis. Differential Geometry is a corequisite.