A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is
We define globally hypoelliptic smooth R k actions as actions whose leafwise Laplacian along the orbit foliation is a globally hypoelliptic differential operator. When k = 1, strong global rigidity is conjectured by Greenfield-Wallach and Katok: every globally hypoelliptic flow is smoothly conjugate to a Diophantine flow on the torus. The conjecture has been confirmed for all homogeneous flows on homogeneous spaces  . In this paper we conjecture that among homogeneous R k actions (k ≥ 2) ondoi:10.3934/dcds.2020164 fatcat:tg72yn67vzfkrjntrzy6e73wke