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Disertación de Maestría
DOI
Documento
Autor
Nombre completo
Reinaldo Resende de Oliveira
Dirección Electrónica
Instituto/Escuela/Facultad
Área de Conocimiento
Fecha de Defensa
Publicación
São Paulo, 2019
Director
Tribunal
Terra, Glaucio (Presidente)
Lodovici, Sinuê Dayan Barbero
Silva, Márcio Fabiano da
Título en inglés
Regularity of almost minimizing sets
Palabras clave en inglés
Almost minimizing
Caccioppoli
Finite perimeter
Geometric measure theory
Locally finite perimeter
Minimizing
Regularity theory
Resumen en inglés
This work was motivated by the famous Plateau's Problem which concerns the existence of a minimizing set of the area functional with prescribed boundary. In order to solve the Plateau's Problem, we make use of different theories: the theory of varifolds, currents and locally finite perimeter sets (Caccioppoli sets). Working on the Caccioppoli sets theory, it is straightforward to prove the existence of a minimizing set in some classical problems as the isoperimetric and Plateau's problems. If we switch the problem to find the regularity that we can extract of some minimizing set, we come across complicated ideas and tools. Although, the Plateau's Problem and other classical problems are well settled. Because of that, we have extensively studied the almost minimizing condition ((; r)-minimizing sets) considered by Maggi ([?]) which subsumes some classical problems. We focused on the regularity theory extracted from this almost minimizing condition.
Título en portugués
Regularidade dos conjuntos quase minimizantes
Palabras clave en portugués
Caccioppoli
Minimizante
Perímetro finito
Perímetro localmente finito
Quase minimizante
Teoria da regularidade
Teoria geométrica da medida
Resumen en portugués
This work was motivated by the famous Plateau's Problem which concerns the existence of a minimizing set of the area functional with prescribed boundary. In order to solve the Plateau's Problem, we make use of different theories: the theory of varifolds, currents and locally finite perimeter sets (Caccioppoli sets). Working on the Caccioppoli sets theory, it is straightforward to prove the existence of a minimizing set in some classical problems as the isoperimetric and Plateau's problems. If we switch the problem to find the regularity that we can extract of some minimizing set, we come across complicated ideas and tools. Although, the Plateau's Problem and other classical problems are well settled. Because of that, we have extensively studied the almost minimizing condition ((; r)-minimizing sets) considered by Maggi ([?]) which subsumes some classical problems. We focused on the regularity theory extracted from this almost minimizing condition.
 
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dissertacao.pdf (826.31 Kbytes)
Fecha de Publicación
2019-09-03
 
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