MATH 597, TOPICS IN RIEMANNIAN GEOMETRY

Syllabus

Class: MWF 10:10–11:00, Room 014 Henderson

Office hours: Wed. 2:30–3:30, McAlister 333

Something to read:

Meyer, Toponogov's theorem and applications

Cheeger and Ebin, Comparison theorems in Riemannian geometry

Berger M. A Panoramic View of Riemannian Geometry

Eschenburg, Local convexity and nonnegative curvature—Gromov's proof of the sphere theorem.

Micallef and Moore, Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-planes.

Buser and Gromoll, On the almost negatively curved 3-sphere.

Kleiner, An isoperimetric comparison theorem.

Croke, A sharp 4-dimensional isoperimetric inequality.

Buser and Karcher, The Bieberbach case in Gromov's almost flat manifold theorem.

Gromov and Thurston, Pinching constants for hyperbolic manifolds.

Berger, Filling Riemannian manifolds or Isosystolic inequalities.