Classes of globally solvable involutive systems

Autor(es)

Bergamasco, Adalberto ^[1] ; Parmeggiani, Alberto ^[2] ; Zani, Sergio ^[1] ; Zugliani, Giuliano ^{[3, 1]}

Afiliação do(s) autor(es)

^[1] ICMC USP, Dept Matemat, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil

^[2] Univ Bologna, Dipartimento Matemat, Piazza Porta S Donato 5, I-40126 Bologna - Italy

^[3] Univ Fed Sao Carlos, Dept Matemat, Caixa Postal 676, BR-13565905 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS; v. 8, n. 4, p. 551-583, DEC 2017.
• Citações Web of Science: 4

Resumo

We study a linear operator associated with a real smooth closed non-exact 1-form b defined on a closed orientable surface. Locally the operator can be seen as an overdetermined system of first order linear partial differential equations. Here we present a result that completely characterizes a class of systems that are globally solvable, namely when b has rank equal to 1, in terms of a topological condition. Such a condition bears on the superlevel and sublevel sets of primitives of b. In a certain covering space, called minimal covering space, the condition is equivalent to the connectedness of the superlevel and sublevel sets of the primitives there defined (a property that frequently appears in related papers). We furthermore exhibit another class of globally solvable systems by constructing smooth closed non-exact 1-forms of arbitrary rank on surfaces of genus greater than 1 out of 1-forms which individually define globally solvable systems on tori. (AU)

• Processo FAPESP: 10/52497-8 - Propriedades globais de sistemas involutivos em variedades compactas.
• Beneficiário: Giuliano Angelo Zugliani
• Modalidade de apoio: Bolsas no Brasil - Doutorado
• Processo FAPESP: 12/05355-9 - Propriedades globais de sistemas involutivos em variedades compactas
• Beneficiário: Giuliano Angelo Zugliani
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Doutorado
• Processo FAPESP: 12/03168-7 - Teoria geométrica de EDP e várias variáveis complexas
• Beneficiário: Jorge Guillermo Hounie
• Modalidade de apoio: Auxílio à Pesquisa - Temático