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http://hdl.handle.net/2445/202966| Title: | El problema de Yamabe |
| Author: | Domingo Pasarin, Joan |
| Director/Tutor: | Ros, Xavier |
| Keywords: | Equacions en derivades parcials Treballs de fi de grau Equacions diferencials el·líptiques Varietats (Matemàtica) Geometria de Riemann Partial differential equations Bachelor's theses Elliptic differential equations Manifolds (Mathematics) Riemannian geometry |
| Issue Date: | 6-Jun-2023 |
| Abstract: | [en] Posed by Hidehiko Yamabe in 1960, the Yamabe problem asks whether it is possible to deform the metric of a given riemannian manifold so that its scalar curvature becomes constant. This problem can be reformulated in terms of a partial differential equation which makes it interesting from an analytical point of view. In this work we aim to study the Yamabe problem in a variational way in order to find a solution when the scalar curvature is non-positive. To do so, we study Sobolev spaces and the critical value of the Rellich-Kondrakov embedding theorem toghether with its close connection with the solution of the Yamabe equation. |
| Note: | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Xavier Ros |
| URI: | http://hdl.handle.net/2445/202966 |
| Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| tfg_joan_domingo_pasarin.pdf | Memòria | 666.3 kB | Adobe PDF | View/Open |
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