Banca de DEFESA: DANIEL DA COSTA SILVA
Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.STUDENT : DANIEL DA COSTA SILVA
DATE: 16/01/2024
TIME: 10:30
LOCAL: Instituto de matemática
TITLE:
Rigidity of asymptotically flat half-spaces
KEY WORDS:
Inverse Mean Curvature Flow with Boundary. Capacity. Statics Manifolds with Boundary. Stable. CMC.
PAGES: 62
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUBÁREA: Geometria e Topologia
SPECIALTY: Geometria Diferencial
SUMMARY:
In the first part of this thesis, we investigate a mass-capacity type inequality for complete and smooth three-dimensional asymptotically flat half-spaces with non-negative scalar curvature and mean convex boundary. In the case of equality, we prove that the manifold is isometric to the Schwarzschild half-space. In the second part, we address static manifolds with boundary and demonstrate that their static potentials do not change sign, provided they are bounded and vanish at the horizon. Furthermore, we deduce an estimate relating the asymptotic expansion and the modified Hawking mass. In the case of equality, the manifold is isometric to R3+. Finally, in a reinterpretation of a result by Galloway-Cederbaum for photon spheres and under assumptions on Gaussian and mean curvatures, we establish a result stating that a compact and static manifold is isometric to a portion of Schwarzschild space.
COMMITTEE MEMBERS:
Presidente - 2346806 - CICERO TIARLOS NOGUEIRA CRUZ
Interno(a) - 2395847 - ABRAAO MENDES DO REGO GOUVEIA
Interno(a) - 2474631 - MARCIO HENRIQUE BATISTA DA SILVA
Externo(a) ao Programa - 2346971 - MARCOS RANIERI DA SILVA - UFALExterno(a) à Instituição - Leandro de Freitas Pessoa - UFPI
Externo(a) à Instituição - MARIA DE ANDRADE COSTA E SILVA