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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Geometrical proofs for the global solvability of systems

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Author(s):
Bergamasco, Adalberto Panobianco [1] ; Parmeggiani, Alberto [2] ; Zani, Sergio Luis [1] ; Zugliani, Giuliano Angelo [1, 3]
Total Authors: 4
Affiliation:
[1] Univ Sao Paulo, Dept Matemat, ICMC, BR-13560970 Sao Carlos, SP - Brazil
[2] Univ Bologna, Dept Math, I-40126 Bologna - Italy
[3] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP - Brazil
Total Affiliations: 3
Document type: Journal article
Source: Mathematische Nachrichten; v. 291, n. 16, p. 2367-2380, NOV 2018.
Web of Science Citations: 1
Abstract

We study a linear operator associated with a closed non-exact 1-form b defined on a smooth closed orientable surface M of genus g > 1. Here we present two proofs that reveal the interplay between the global solvability of the operator and the global topology of the surface. The first result brings an answer for the global solvability when the system is defined by a generic Morse 1-form. Necessary conditions for the global solvability bearing on the sublevel and superlevel sets of primitives of a smooth 1-form b have already been established; we also present a more intuitive proof of this result. (AU)

FAPESP's process: 12/05355-9 - Global properties of involutive systems on compact manifolds
Grantee:Giuliano Angelo Zugliani
Support type: Scholarships abroad - Research Internship - Doctorate
FAPESP's process: 12/03168-7 - Geometric theory of PDE and several complex variables
Grantee:Jorge Guillermo Hounie
Support type: Research Projects - Thematic Grants