# MATH 760: Problems in Geometric Analysis

Spring 2015

University of
Pennsylvania

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**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