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Master's Dissertation
DOI
Document
Author
Full name
Reinaldo Resende de Oliveira
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2019
Supervisor
Committee
Terra, Glaucio (President)
Lodovici, Sinuê Dayan Barbero
Silva, Márcio Fabiano da
Title in English
Regularity of almost minimizing sets
Keywords in English
Almost minimizing
Caccioppoli
Finite perimeter
Geometric measure theory
Locally finite perimeter
Minimizing
Regularity theory
Abstract in English
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.
Title in Portuguese
Regularidade dos conjuntos quase minimizantes
Keywords in Portuguese
Caccioppoli
Minimizante
Perímetro finito
Perímetro localmente finito
Quase minimizante
Teoria da regularidade
Teoria geométrica da medida
Abstract in Portuguese
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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Publishing Date
2019-09-03
 
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