Existência e análise de Blow-up de métricas conformes com curvaturas escalar e média prescritas - Gomes, Dalton da Silva (2024)
The objective of this dissertation is to present with nuances the results obtained in [9], in which it studies the problem of prescribing the scalar and mean curvatures in Riemannian manifolds with boundary aM and dimension n ≥ 3 through of conformal metrics. This is a variational problem whose analysis is linked to a relationship between the functions that we want to prescribe as scalar and mean curvatures. This relationship is given by a certain function Dn defined on the boundary aM. If Dn < 1, the solution is found through minimization of a certain functional. The case where Dn > 1 at some point requires a blow-up analysis. In this case, some results are only obtained for dimension 3.