Abstract
AbstractWe provide criteria for local unsolvability of first-order differential systems induced by complex vector fields employing techniques from the theory of locally integrable structures. Following Hörmander’s approach to study locally unsolvable equations, we obtain analogous results in the differential complex associated to a locally integrable structure provided that it is not locally exact in three different scenarios: top-degree, Levi-nondegenerate structures and co-rank 1 structures.
Funder
Conselho Nacional de Desenvolvimento Científico e Tecnológico
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Numerical Analysis,Analysis
Reference34 articles.
1. Andreotti, A., Fredricks, G.A., Nacinovich, M.: On the absence of Poincaré lemma in tangential Cauchy-Riemann complexes. Ann. Scuola Norm.-Sci. Ser. 4 8(3), 365–404 (1981)
2. Andreotti, A., Hill, C.D.: E. E. Levi convexity and the Hans Lewy problem. Part II : vanishing theorems. Ann. Scuola Norm.-Sci. Ser. 3 26(4), 747–806 (1972)
3. Baouendi, M.S., Ebenfelt, P., Rothschild, L.P.: Real Submanifolds in Complex Space and Their Mappings. Princeton University Press, Princeton (1999)
4. Barostichi, R.F., Cordaro, P.D., Petronilho, G.: On the Borel property for solutions to systems of complex vector fields. Math. Nachr. 286(14–15), 1439–1451 (2013)
5. Berhanu, S., Cordaro, P.D., Hounie, J.: An Introduction to Involutive Structures, vol. 6. Cambridge University Press, Cambridge (2008)