Compacidade de soluções para equações do tipo Yamabe em dimensão 3 - Silva, Lorena Maria Augusto Pequeno (2019)
In this dissertation, we will prove results on the compactness of solutions for equations of the Yamabe type in Riemannian manifolds of dimension 3. For this, we will do a local analysis of a sequence of solutions near blow-up points and use the Positive Mass Theorem. In addition, we will see some applications about this result: the calculation of the Leray-Schauder degree and the existence and multiplicity of minimizing sequences. Finally, we will see that the same results remain valid for a class of Yamabe type equations with more general weight also in dimension 3.