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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
MathSciNet review:
2367104
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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:
-
- [BT1]
- Baouendi, M. S. and Trèves, F., A local constancy principle for the solutions of certain overdetermined systems of first-order linear partial differential equations, Adv. in Math. Suppl. Stud., 7a, Academic Press, New York-London, (1981), 245-262. MR 634241 (84f:35105)
- [B]
- Bergamasco, A. P., Remarks about global analytic hypoellipticity, Trans. Amer. Math. Soc. 351 (1999), no. 10, 4113-4126. MR 1603878 (99m:35032)
- [BNZ]
- Bergamasco, A., Nunes, W. and Zani, S., Global properties of a class of overdetermined systems, J. Funct. Anal. 200 (2003), no. 1, 31-64. MR 1974087 (2004c:35295)
- [BZ]
- Bergamasco, A. and Zani, S., Prescribing analytic singularities for solutions of a class of vector fields on the torus, Trans. Amer. Math. Soc. 357 (2005), no. 10, 4159-4174. MR 2159704 (2006c:35002)
- [CH]
- Cordaro, P. and Hounie, J., On local solvability of underdetermined systems of vector fields, Amer. J. Math. 112 (1990), 243-270. MR 1047299 (91j:58150)
- [G]
- Grauert, H., On Levi's problem and the imbedding of real-analytic manifolds, Ann. of Math. (2) 68 (1958), 460-472. MR 0098847 (20:5299)
- [Gr]
- Greenfield, S. J., Hypoelliptic vector fields and continued fractions, Proc. Amer. Math. Soc. 31 (1972), 115-118. MR 0301459 (46:617)
- [H]
- Hirsch, M., Differential topology, Graduate Texts in Mathematics, No. 33, Springer-Verlag, New York, 1976. MR 0448362 (56:6669)
- [H1]
- Hounie, J., Minimal sets of families of vector fields on compact surfaces, J. Differential Geom. 16 (1981), no. 4, 739-744. MR 661663 (83j:58075)
- [H2]
- Hounie, J., Globally hypoelliptic vector fields on compact surfaces, Comm. Partial Differential Equations 7 (1982), no. 4, 343-370. MR 652813 (83k:35025)
- [S]
- Sussmann, H., Orbits of families of vector fields and integrability of distributions. Trans. Amer. Math. Soc. 180 (1973), 171-188. MR 0321133 (47:9666)
- [T]
- Treves, F., Hypo-analytic Structures, Princeton University Press, Princeton, NJ, 1992. MR 1200459 (94e:35014)
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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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