On the Greenfield-Wallach and Katok conjectures

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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).
19 pages

Keywords

Dynamical Systems, 37C10, 37C15, 35H10

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/132525

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0706.3981
 http://arxiv.org/abs/0706.3981

Collections

arXiv