Maximum principle for tensors with applications to the Ricci flow

Maximum principle for tensors with applications to the Ricci flow

Thu, 11/11/2010
13:00 		Christopher Hopper (University of Oxford) Junior Geometry and Topology Seminar Add to calendar SR1
Maximum principle for tensors with applications to the Ricci flow
The maximum principle is one of the main tools use to understand the behaviour of solutions to the Ricci flow. It is a very powerful tool that can be used to show that pointwise inequalities on the initial data of parabolic PDE are preserved by the evolution. A particular weak maximum principle for vector bundles will be discussed with references to Hamilton's seminal work [J. Differential Geom. 17 (1982), no. 2, 255–306; MR664497] on 3-manifolds with positive Ricci curvature and his follow up paper [J. Differential Geom. 24 (1986), no. 2, 153–179; MR0862046] that extends to 4-manifolds with various curvature assumptions.