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Transactions of the American Mathematical Society
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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DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1061777-8
PII: S 0002-9947(1992)1061777-8
Article copyright: © Copyright 1992 American Mathematical Society