Some regularity results in geometric measure theory

• Ano de defesa: 2023
• Autor(a) principal: Oliveira, Reinaldo Resende de
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Anisotropic functionals; Area minimizing currents; Conjuntos de perímetro finito; Correntes; Correntes minimizantes de área; Currents; Finite perimeter sets; Funcionais anisotropicos; Geometric measure theory; Plateau problem; Problema de Plateau; Regularity theory; Stationary varifolds; Teoria da regularidade; Teoria geométrica da medida; Varifolds; Varifolds estacionarias
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/45/45131/tde-15092023-152928/

During the authors PhD, the following single-named contributions were made: [RdO22] and [Res23]. Moreover the following articles were written together with his collaborators: [ACN + 22], [NR22], and [RR23]. Since the topics of these works are substantially different, we will present this PhD thesis as a composition of some regularity theorems in geometric measure theory. Specifically, this thesis is an exposition of the results in [NR22], [Res23] and [RR23]. Such papers are unlike in nature, considerably different techniques and theories are used in each of them, however they share the same goal: proving regularity for measure-theoretic objects solving variational problems.