Mathematics 428

This is the homepage for Math 428 (TTh 2:00pm in Lunt 10?), taught by Gui-Qiang Chen, Prof. of Math. Spring Quarter 2002

Office: Lunt 306

Office Hours: By appointment

This is a one-quarter introductory course on the Geometric Measure Theory and its applications. The geometric measure theory has applications in partial differential equations, calculus of variations, differential geometry, dynamical systems, differential topology, mathematical physics, among others. It is planned to start with a quick review of general measure theory in basic real analysis. This is followed by

Introduction of Hausdorff measures

Sobolev functions

BV functions and sets of finite perimeter

Gauss-Green theorem

Differentiability and approximation

Basic references include:

1. ``Geometric Measure Theory'' by Herbert Federer, Classics in Mathematics, Springer-Verlag: 1996; ISBN 3-540-60656-4

2. ``Measure Theory and Fine Properties of Functions'' by Lawrence C. Evans and Ronald F. Gariepy, CRC Press: Boca Raton, Florida, 1992; IBSN 0-8493-7157-0

3. ``Weakly Differentiable Functions'' by William P. Ziemer, Springer-Verlag: New York, 1989.

4. ``Geometric Measure Theory: A Beginners Guide'', by F. Morgan, Academic Press: Boston, 1988