## Geometric Measure Theory and Its Applications

#### October - December 2012, Tuesday 13:00-15:00 Prof. G-Q Chen.

Geometric
Measure Theory has contributed greatly to the development of the calculus of
variations, partial differential equations, and geometric analysis, and has
important applications to differential geometry, stochastic analysis, dynamical
systems, differential topology, mathematical physics,
among others. This course is an introduction to some facets of the theory and
its applications. The course starts with a brief review on basic measure theory
and is followed by the topics including Hausdorff
measures, area/co-area
formulae, Sobolev functions, BV functions, sets of finite perimeter, divergence-measure fields, Gauss-Green
theorems and normal traces,
*differentiability and approximation, *varifolds and
currents, connections with and applications to nonlinear PDEs (the topics with
* are optional, depending on the course development).

Basic
real analysis or the equivalent is the only essential prerequisite. However,
some familiarity with basic measure theory, functional analysis, and
differential geometry is desirable.

*Lecture 5*

*Lecture
6*

*Lecture 7*

*Lecture 8*

* *

*Lecture 9*

###### Topics & References: See Lecture 0