Seminars & Colloquia Calendar
Contrasting Various Notions of Convergence in Geometric Analysis
Brian Allen (United States Military Academy, West Point)
Location: Hill 525
Date & time: Tuesday, 24 April 2018 at 3:30PM - 4:30PM
Abstract: We explore the distinctions between \(L^p\) convergence of metric tensors on a fixed Riemannian manifold vs. GH, uniform, and intrinsic flat convergence of the the resulting sequence of metric spaces. We provide a number of examples which demonstrate these notions of convergence do not agree even for two dimensional warped product manifolds with warping functions converging in the \(L^p\) sense. We then prove a theorem which requires \(L^p\) bounds from above and \(C^0\) bounds from below on the warping functions to obtain enough control for the limits to agree.
This is joint work with Christina Sormani.