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.
Document type: | Dissertation |
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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 > Institut für Mathematik |
DDC-classification: | 510 Mathematics |
Controlled Keywords: | Differentialgeometrie, Partielle Differentialgleichung |