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Globally analytic hypoelliptic vector fields on compact surfaces
Author(s):
Adalberto
P.
Bergamasco;
Sérgio
Luís
Zani
Journal:
Proc. Amer. Math. Soc.
136
(2008),
1305-1310.
MSC (2000):
Primary 35H10, 58GXX
Posted:
November 28, 2007
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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.
References:
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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:
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
Posted:
November 28, 2007
Additional Notes:
The first author was partially supported by CNPq. Both authors were partially supported by FAPESP
Communicated by:
David Tartakoff
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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