Tube Structures of Co-rank 1 with Forms Defined on Compact Surfaces

Autor(es)

Hounie, J. ^[1] ; Zugliani, G. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF GEOMETRIC ANALYSIS; v. 31, n. 3 FEB 2020.
• Citações Web of Science: 0

Resumo

We study the global solvability of a locally integrable structure of tube type and co-rank 1 by considering a linear partial differential operator L associated to a general complex smooth closed 1-form c defined on a smooth closed n-manifold. The main result characterizes the global solvability of L when n = 2 in terms of geometric properties of a primitive of a convenient exact pullback of the form Im(c) as well as in terms of homological properties of Re(c) related to small divisors phenomena. Although the full characterization is restricted to orientable surfaces, some partial results hold true for compact manifolds of any dimension, in particular, the necessity of the conditions, and the equivalence when Im(c) is exact. We also obtain informations on the global hypoellipticity of L and the global solvability of Ln-1-the last non-trivial operator of the complex when M is orientable. (AU)

• Processo FAPESP: 18/14316-3 - Teoria geométrica de EDP e análise complexa multidimensional
• Beneficiário: Paulo Domingos Cordaro
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 14/23748-3 - Sistemas involutivos e resolubilidade global
• Beneficiário: Giuliano Angelo Zugliani
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado