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:
http://www.ams.org/notices/200310/fea-milnor.pdf
http://www.ams.org/journals/bull/2005-42-01/S0273-0979-04-01045-6/S0273-0979-04-01045-6.pdf
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