Mathematics Graduate Student Colloquium

MGSC Website: http://math.uci.edu/~mgsc/

Applications of the gradient estimate on noncompact manifolds

Ovidiu Munteanu
Wednesday, October 10, 2007
5:00 pm - 5:50 pm
MSTB 124

Talk Abstract:

We will discuss an estimate that is essential in the study of harmonic functions on manifolds. The gradient estimate was proved by S. T. Yau (Fields Medal recipient and distinguished guest of the UCI math department last year) more than 30 years ago using a maximum principle argument. An important application is that manifolds with nonnegative Ricci curvature satisfy the Liouville property. The maximum principle method has since been used in many other situations, for example to prove eigenvalue estimates for the Laplace operator or to prove parabolic versions of the gradient estimate. Recently, P. Li and J. Wang improved the gradient estimate of Yau and obtained a sharp version. We will give a short account of these results and their applications.

About the Speaker:

Ovidiu is a fourth year graduate student at UCI. He received his B.S. in mathematics at Transylvania University in Romania in 2002. Ovidiu's research interest is in Differential Geometry and Partial Differential Equations.

Refreshments:

Pizza will be served after the talk.