Subvariedades com bordo livre em bolas de formas espaciais

• Ano de defesa: 2022
• Autor(a) principal: Roney Pereira dos Santos
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Minas Gerais; Brasil; ICX - DEPARTAMENTO DE MATEMÁTICA; Programa de Pós-Graduação em Matemática; UFMG
• Palavras-chave em Português: Problema de bordo livre; Superfície mínima; Desigualdade geométrica; Resultado de rigidez; Matemática – Teses; Subvariedades – Teses; Superfícies (Matemática)i – Teses; Desigualdades (Matemática).
• Link de acesso: http://hdl.handle.net/1843/59121

In this thesis, we would like to investigate the behavior of hypersurfaces with free boundary in the context of geodesic balls in space forms. Firstly, we are interested in understanding how the boundary condition affects the geometries along the boundary of hypersurfaces viewed both the original hypersurface and the sphere delimiting the ball in question. With these relations, we will be able to find two integral inequalities. One of these inequalities provides a relation between the geometry and topology of these hypersurfaces in the dimension three case. Others applications of the equations along the free boundary are a identity that counts the umbilical points (with multiplicities) of the surface according with its topology, the recovery of the Nitsche Theorem, an equivalence between the topology and the existence of umbilic points on the surface, and a reformulation of the Catenoid Conjecture.