Cornell Math - MATH 614, Spring 2004

MATH 614: Aspects of Analysis on Metric Measure Spaces (Spring 2004)

Instructor: Laurent Saloff-Coste

Meeting Time & Room

We will give an introduction to analysis on measure metric spaces and discuss the doubling property, covering lemmas, upper-gradients, Poincare and Sobolev inequalities, p-parabolicity, Dirichlet spaces, the intrinsic distance, Harnack inequality, and Heat kernel estimates.

Relevant textbooks are:

• Heinonen, Juha: Lectures on analysis on metric spaces. Universitext. Springer-Verlag, New York, 2001.
• Hajlasz, Piotr; Koskela, Pekka: Sobolev met Poincaré. Mem. Amer. Math. Soc. 145 (2000), no. 688.
• Saloff-Coste, Laurent: Aspects of Sobolev type inequalities. London Math. Soc. Lecture Note Series 289, Cambridge University press (2002).