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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The Mizohata structure on the sphere

Author: Jorge Hounie
Journal: Trans. Amer. Math. Soc. 334 (1992), 641-649
MSC: Primary 32F40; Secondary 58G05
MathSciNet review: 1061777
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Abstract: We prove that a compact surface that admits a Mizohata structure is (homeomorphic to) a sphere and that there exists exactly one such structure $ \mathcal{L}$ up to conjugation by diffeomorphisms. We also characterize the range and the kernel of the operator $ {\delta _0}$ induced by $ \mathcal{L}$ , i.e., obtained from the exterior derivative on functions by passing to the quotient modulo $ {\mathcal{L}^\bot }$ .

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  • [1] M. S. Baouendi and F. Treves, A property of the functions and distributions annihilated by a locally integrable system of complex vector fields, Ann. of Math. (2) 113 (1981), 387-421. MR 607899 (82f:35057)
  • [2] A. Bergamasco, P. Cordaro, and J. Hounie, Global properties of a class of vector fields in the plane, J. Differential Equations 74 (1988), 179-199. MR 952894 (89h:58175)
  • [3] P. R. Garabedian, An unsolvable equation, Proc. Amer. Math. Soc. 25 (1970), 207-208. MR 0252809 (40:6026)
  • [4] Ch. Pommerenke, Univalent functions, Vandehoeck & Ruprecht, 1975. MR 0507768 (58:22526)
  • [5] F. Treves, Remarks about certain first-order linear P.D.E. in two variables, Comm. Partial Differential Equations 5 (1980), 381-425. MR 567779 (83e:35033)

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Article copyright: © Copyright 1992 American Mathematical Society

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