Dynamics Seminar: Rigidity and Finiteness of Totally Geodesic Hypersurfaces in Negative Curvature, by Ben Lowe
September 18, 2024
3:00 PM - 3:50 PM
Ben Lowe (University of Chicago): Rigidity and Finiteness of Totally Geodesic Hypersurfaces in Negative Curvature
This talk will discuss progress towards answering the following question: if a closed negatively curved manifold M has infinitely many totally geodesic hypersurfaces, then must it have constant curvature (and thus, by work of Bader-Fisher-Stover-Miller and Margulis-Mohammadi, be homothetic to an arithmetic hyperbolic manifold)? First, I will talk about work that gives a partial answer to this question under the assumption that M is hyperbolizable. This part uses Ratners theorems in an essential way. I will also talk about work that gives an affirmative answer to the question if the metric on M is analytic. In this case the analyticity condition together with properties of the geodesic flow in negative curvature allow us to conclude what in constant curvature would follow from Ratners theorems. This talk is based on joint work with Fernando Al Assal, and Simion Filip and David Fisher.
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Date posted
Aug 30, 2024
Date updated
Aug 30, 2024
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