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Dual flows in hyperbolic space and de Sitter space

Yu, Hao

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Abstract

We consider contracting flows in (n+1)-dimensional hyperbolic space and expanding flows in (n+1)-dimensional de Sitter space. When the flow hypersurfaces are strictly convex we relate the contracting hypersurfaces and the expanding hypersurfaces by the Gauß map. The contracting hypersurfaces shrink to a point in finite time while the expanding hypersurfaces converge to the maximal slice {\tau = 0}. After rescaling, by the same scale factor, the rescaled contracting hypersurfaces converge to a unit geodesic sphere, while the rescaled expanding hypersurfaces converge to slice {\tau = −1} exponentially fast.

Item Type: Dissertation
Supervisor: Gerhardt, Prof. Dr. Claus
Date of thesis defense: 5 May 2017
Date Deposited: 10 Oct 2017 11:49
Date: 2017
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 510 Mathematics
Controlled Keywords: Differentialgeometrie, Partielle Differentialgleichung
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