Math 18.966: Geometry of Manifolds II

Tuesday, Thursday, 9:30-11am, 2-147

Course website:


Tristan Collins
Email: tristanc at math dot mit dot edu
Office: 2-273

About the course

This course will cover aspects of comparison geometry, Ricci curvature, and the convergence theory of Riemannian manifolds as well as some applications.


The syllabus for the course is available here .

Course References


This is approximate. I will attempt to keep track of all the references used in class.

Date Material Problems/Handouts
Feb.5--26 Geometry of generalized distance functions: References (K)
Homework 1
Feb. 28--Mar. 14 Toponogov's Theorem, Gromov-Hausdorff Convergence: References (K), (Pet) Homework 2
Mar. 19- Apr. 5 Elliptic PDE: The maximum princple, regularity in Sobolev spaces, Schauder theory (Ev), (GT), (LH), (Sz). Applications ot Hodge theory (Pet) Homework 3
Apr. 9- 11 Cheeger-Gromoll splitting (Ch)
Apr. 16-23 Harmonic coordinates Existence of Harmonic coordinates, Fundamental compactness theorem of Riemannian manifolds (Pet)
Apr. 25-- Applications Anderson's estimate for Harmonic radius (An), Cheeger's finiteness theorem (Pet) Homework 4