Ros, XavierDomingo Pasarin, Joan2023-10-192023-10-192023-06-06https://hdl.handle.net/2445/202966Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Xavier Ros[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.54 p.application/pdfcatcc-by-nc-nd (c) Joan Domingo Pasarin, 2023http://creativecommons.org/licenses/by-nc-nd/3.0/es/Equacions en derivades parcialsTreballs de fi de grauEquacions diferencials el·líptiquesVarietats (Matemàtica)Geometria de RiemannPartial differential equationsBachelor's thesesElliptic differential equationsManifolds (Mathematics)Riemannian geometryinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess