MATH 760: Problems in Geometric Analysis

  Spring 2015

University of Pennsylvania

Course Information

Primary Textbook:
Some Nonlinear Problems in Riemannian Geometry, T. Aubin

Some Background Material:

Riemannian Geometry, M. do Carmo
Topology and Geometry
, G. Bredon
Geometric Measure Theory, H. Federer
Einstein Manifolds, A. Besse
Elliptic Partial Differential Equations of Second Order, D. Gilbard and N. Trudinger

Additional Reading:
East-to-read survey articles on geometrization and Ricci flow:

Information on the Sobolev constant and isoperimetric constant:
Croke, Some Isoperimetric Inequalities and Eigenvalue Estimates, (1980)
Osserman, The Isoperimetric Inequality, (1978)

Analytic theory of Einstein manifolds:
Anderson, Ricci curvature bounds and Einstein metrics on compact manifolds, (1989)
Bando-Kasue-Nakajima, On a construction of Coordinates at Infinity on Manifolds with Fast Curvature Decay and Maximal Volume Growth, (1990)

Theory of Harmonic Coordinates:
DeTurck-Kazdan, Some Regularity Theorems in Riemannian Geometry, (1981)
Greene-Wu, Lipschitz Convergence of Riemannian Manifolds, (1988)

Supplimental Notes, with practice problems

Instructor: Brian Weber, brweber AT math dot upenn dot edu
Office: DRL 4N67
Office Hours: Mondays and Wednesdays before class