Regularity of almost minimizing sets

• Autor(a) principal: Oliveira, Reinaldo Resende de
• Data de Publicação: 2019
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: http://www.teses.usp.br/teses/disponiveis/45/45131/tde-28082019-125158/
• topic: Almost minimizing; Caccioppoli; Caccioppoli; Finite perimeter; Geometric measure theory; Locally finite perimeter; Minimizante; Minimizing; Perímetro finito; Perímetro localmente finito; Quase minimizante; Regularity theory; Teoria da regularidade; Teoria geométrica da medida

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.