On the Greenfield-Wallach and Katok conjectures

Details On the Greenfield-Wallach and Katok conjectures On the Greenfield-Wallach and Katok conjectures

2007-06-27

arxiv.org/abs/0706.3981v1

Mathematics

Dynamical Systems

19 pages

Scientific paper

We survey recent progress on the Greenfield-Wallach and Katok conjectures on globally hypoelliptic and cohomology free vector fields and derive a proof of the conjectures in dimension three. The argument is primarily based on recent work of F. and J. Rodriguez Hertz which allows us to reduce the question to the case of a Reeb flow for a contact form. The contact case is settled by invoking the Weinstein conjecture (which has been recently announced by C. Taubes).

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