In this thesis we study the evolution of mass of asymptotically hyperbolic manifolds underRicci flow, following Balehowski and Woolgar [5]. Relying on Bahuaud [2] we assume shorttimeexistence of the flow, and derive the equations describing how the geometry of themanifold near infinity changes under the flow. In turn, we use these equations to findthe formula describing the evolution of the mass under the Ricci flow, in particular itsexponential decay in time. As an application, we discuss (again, following Balehowski andWoolgar [5]) how the Ricci flow technique can be used to prove the rigidity part of thepositive mass theorem for asymptotically hyperbolic manifolds.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:uu-488599 |
| Date | January 2022 |
| Creators | Hjort, Oliver |
| Publisher | Uppsala universitet, Geometri och fysik |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | U.U.D.M. project report ; 2022:31 |
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