Geometry/topology Seminar
Monday, September 12, 2022, 3:15pm, Physics 119
Demetre Kazaras (Duke University)
Comparison geometry and spacetime harmonic functions
Abstract:- Comparison theorems are the basis for our geometric understanding of Riemannian manifolds satisfying a given curvature condition. A remarkable example is the Gromov-Lawson torus band inequality, which bounds the distance between the two sides of a Riemannian torus-cross-interval with positive scalar curvature by a sharp constant. We will give a new qualitative version of this and similar band-type inequalities in dimension 3 using the notion of spacetime harmonic functions, which recently played the lead role in our new proof of the positive mass theorem. Other applications include new versions of Bonnet-Myer's diameter estimate and Llarull's theorem which do not require a completeness assumption. This is joint work with Sven Hirsch, Marcus Khuri, and Yiyue Zhang.
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