O teorema da aplicação inversa e aplicações

• Ano de defesa: 2022
• Autor(a) principal: Zacarias, André Pinheiro da Silva
• Orientador(a): Melo, Marcos Ferreira de
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Palavras-chave em Português: Teorema da aplicacão inversa; Teorema da função implícita; Multiplicadores de Lagrange; Forma local das imersões; Forma local das submersões; Superfícies euclidianas; Variedades diferenciáveis; Inverse application theorem; Implicit function theorem; Lagrange multipliers; Local form of immersions; Local form of submersions; Euclidean surfaces; Differentiable manifolds
• Link de acesso: http://www.repositorio.ufc.br/handle/riufc/70186

The Inverse Application Theorem (IAT) is an important analysis result that establishes, even if locally, the existence of a continuously differentiable inverse map. Given its importance, this work aims to show in detail its demonstration. Before, we will expose all the necessary prerequisites and, soon after, we will analyze some applications such as the Implicit Function Theorem and the Lagrange multipliers method. In order to give a broader idea and show that the TAI is valid in other environments, we will give a basic but sufficient view of Euclidean surfaces and then we will enunciate and give the due proof of the TAI between Euclidean surfaces of the same dimension. From there we will further extend our environment to differentiable manifolds.