TITLE: Ricci flow on non-compact Riemannian manifolds and curvature
concentration.
ABSTRACT: The Ricci flow on Riemannian manifolds was introduced by Richard
Hamilton in 1982 to approach fundamental problems in topology & geometry
with parabolic PDE methods. It has since been applied successfully to
longstanding problems on compact and non-compact manifolds. In this talk I
will review the development of basic Ricci flow theory on complete
non-compact manifolds then focus on the assumption of integral/weak
curvature bounds. Results on long-time existence and convergence of the
flow will provided when the initial Riemannian manifold satisfies certain
scale-invariant conditions. The talk is based on joint work with Adam
Martens.