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Globally hypoelliptic vector fields on compact surfaces. (English) Zbl 0588.35064
Let M be a compact, connected, orientable, two-dimensional smooth manifold. If L is a globally hypoelliptic vector field on M, then either M is the closure of a one-dimensional L-orbit or L satisfies the Nirenberg-Trèves condition (P), and the group of diffeomorphisms G generated by Re L and Im L acts transitively.

MSC:
35M99 Partial differential equations of mixed type and mixed-type systems of partial differential equations
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