PDE Geometric Analysis seminar

The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.

Seminar Schedule Fall 2012

date	speaker	title	host(s)
September 17	Bing Wang (UW Madison)	On the regularity of limit space	local
October 15	Peter Polacik (U of M)	Exponential separation between positive and sign-changing solutions and its applications	Zlatos

Abstracts

Bing Wang (UW Madison)

On the regularity of limit space

This is a joint work with Gang Tian. In this talk, we will discuss how to improve regularity of the limit space by Ricci flow. We study the structure of the limit space of a sequence of almost Einstein manifolds, which are generalizations of Einstein manifolds. Roughly speaking, such manifolds are the initial manifolds of some normalized Ricci flows whose scalar curvatures are almost constants over space-time in the L1-sense, Ricci curvatures are bounded from below at the initial time. Under the non-collapsed condition, we show that the limit space of a sequence of almost Einstein manifolds has most properties which is known for the limit space of Einstein manifolds. As applications, we can apply our structure results to study the properties of K¨ahler manifolds.

Peter Polacik (University of Minnesota)

Exponential separation between positive and sign-changing solutions and its applications

In linear nonautonomous second-order parabolic equations, the exponential separation refers to the exponential decay of any sign-changing solution relative to any positive solution. In this lecture, after summarizing key results on exponential separation, we show how it can be effectively used in studies of some nonlinear parabolic problems.