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Topology/Geometry Seminar

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.

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