Global Mizohata structures

  • Howard Jacobowitz

DOI: 10.1007/BF02921581

Cite this article as:
Jacobowitz, H. J Geom Anal (1993) 3: 153. doi:10.1007/BF02921581


The Mizohata partial differential operator is generalized to global structures on compact two-dimensional manifolds. A generalization of the Hopf Theorem on vector fields is used to show that a first integral can exist if and only if the genus is even. The Mizohata structures on the sphere are classified by the diffeomorphism group of the circle modulo the Moebius subgroup and a necessary and sufficient condition, expressed in terms of the associated diffeomorphism, is given for the existence of a first integral.

Math Subject Classification


Key Words and Phrases

CRdiffeomorphism group of the circleEuler characteristicHopf Theoremglobal differential operatorMizohataMoebius transformationnonsolvable

Copyright information

© CRC Press, Inc 1993

Authors and Affiliations

  • Howard Jacobowitz
    • 1
  1. 1.Department of MathemeticsRutgers UniversityCamdenUSA