Hounie, J. Globally hypoelliptic vector fields on compact surfaces. (English) Zbl 0588.35064 Commun. Partial Differ. Equations 7, 343-370 (1982). 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. Cited in 31 Documents MSC: 35M99 Partial differential equations of mixed type and mixed-type systems of partial differential equations Keywords:globally hypoelliptic vector; Nirenberg-Trèves condition PDF BibTeX XML Cite \textit{J. Hounie}, Commun. Partial Differ. Equations 7, 343--370 (1982; Zbl 0588.35064) Full Text: DOI OpenURL References: [1] Cardoso F., J. Diff. Equations 33 (2) pp 239– (1979) · Zbl 0377.35013 [2] Duistermaat J., Acta Math. 128 pp 183– (1972) · Zbl 0232.47055 [3] Greenfield S., Topology 12 pp 247– (1973) · Zbl 0268.58007 [4] Hörmander L., Ann. of Math. 108 pp 569– (1978) · Zbl 0396.35087 [5] Hounie J., Advances in Math. [6] Hounie J., J. Diff. Geometry [7] Nagano T., J. Math. Soc. Japan 18 (4) pp 398– (1966) · Zbl 0147.23502 [8] Sternberg S., Part II, W. A. Benjamin (1969) [9] Strauss M., J. Diff. Equations 15 pp 195– (1974) · Zbl 0266.35009 [10] Sussmann H., Trans. Amer. Math. Soc. 180 pp 171– (1973) [11] Treves F., Ann. Scu. Norm. Sup. Pisa 4 (3) pp 171– (1976) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.