Hypersurfaces with prescribed scalar curvature in geometric flows
We consider translators to the extrinsic fl ow defi nedby S α in R × hPn or in Pn × χR , where S is the extrinsic scalar curvature, α ∈ {1/2,1}, and n ≥ 3. We show that there exist rotational bowl-type and translating catenoid-type translators in P × χR . In our main existence results we exhibit a o...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | Brasil |
| Institución: | Universidade Federal do Ceará (UFC) |
| Repositorio: | Repositório Institucional da Universidade Federal do Ceará (UFC) |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.ufc.br:riufc/72247 |
| Acceso en línea: | http://www.repositorio.ufc.br/handle/riufc/72247 |
| Access Level: | acceso abierto |
| Palabra clave: | Fluxo pela curvatura escalar Translator Princípios do máximo (Matemática) Scalar curvature flow Maximum principle |
| Sumario: | We consider translators to the extrinsic fl ow defi nedby S α in R × hPn or in Pn × χR , where S is the extrinsic scalar curvature, α ∈ {1/2,1}, and n ≥ 3. We show that there exist rotational bowl-type and translating catenoid-type translators in P × χR . In our main existence results we exhibit a one-parameter family of explicit solutions when α = 1/2 in P × χR when P is Hadamard complete manifold with a rotationally symmetric metric. We discuss the variational nature of solitons, we fi nd a one-parameter family of null scalar curvature hypersurfaces when P × χR is Einstein, we use maximum principle to show that if a translating soliton is contained in a slab in I × hP and it is parabolic with respect to the L map then it is contained in a leaf P s = {s} × P and that if P × χR has constant sectional curvature and a translating soliton is parabolic with respect to L ζ map then it is not bounded from above. |
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