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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Globally analytic hypoelliptic vector fields on compact surfaces


Authors: Adalberto P. Bergamasco and Sérgio Luís Zani
Journal: Proc. Amer. Math. Soc. 136 (2008), 1305-1310
MSC (2000): Primary 35H10, 58GXX
Published electronically: November 28, 2007
MathSciNet review: 2367104
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Abstract | References | Similar Articles | Additional Information

Abstract: We present a characterization of the global analytic hypoellipticity of a complex, non-singular, real analytic vector field defined on a compact, connected, orientable, two-dimensional, real analytic manifold.

In particular, we show that such vector fields exist only on the torus.


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Additional Information

Adalberto P. Bergamasco
Affiliation: Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação - USP, Caixa Postal 668, São Carlos, SP, 13560-970, Brasil
Email: apbergam@icmc.usp.br

Sérgio Luís Zani
Affiliation: Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação - USP, Caixa Postal 668, São Carlos, SP, 13560-970, Brasil
Email: szani@icmc.usp.br

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09097-1
PII: S 0002-9939(07)09097-1
Keywords: Complex vector fields, global analytic hypoellipticity, Liouville numbers, sheaf cohomology, Sussmann orbits
Received by editor(s): January 22, 2007
Published electronically: November 28, 2007
Additional Notes: The first author was partially supported by CNPq. Both authors were partially supported by FAPESP
Communicated by: David Tartakoff
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.