MA 336: Topics in Riemannian Geometry
Credits: 3:0
Prerequisite courses: MA 333 - Riemannian Geometry
Bochner formula, Laplace comparison, Volume comparison, Heat kernel estimates, Cheng-Yau gradient estimates, Cheeger-Gromoll splitting theorem, Gromov-Haudorff convergence, epsilon regularity, almost rigidity, quantitative structure theory of Riemannian manifolds with Ricci curvature bounds. If time permits, we will discuss the proof of the co-dimension four conjecture due to Cheeger and Naber.
Suggested books and references:
- Peter Petersen, Riemannian geometry, Graduate Texts in Mathematics, 171. Springer-Verlag, New York, 1998.
- Richard Schoen and ST Yau, Lectures of Differential Geometry, International Press, 1997.
- Jeff Cheeger, Degenerations of Riemannian metrics under Ricci curvature bounds, Publications of the Scuola Normale Superiore, Birkhauser, 2001.