Mathematical Research Letters

Volume 1, Issue 2, March 1994 pp. 193-202.

Subelliptic Estimates of Polynomial Differential Operators and Applications to Rigidity of Abelian Actions

Authors: A. Katok and R. J. Spatzier
Author institution: The Pennsylvania State University, and University of Michigan

Summary: We use subelliptic estimates for certain polynomial differential operators to show $C^{\infty}$-regularity of distributions smooth ``along'' foliations which satisfy a certain non-degeneracy condition and whose sum is totally non-integrable. We use this to extend the cocycle trivialization theorem for Anosov actions of higher rank abelian groups \cite{KS0} to certain partially hyperbolic actions of ${\bbb Z}^k$ or ${\bbb R}k$ for $k \geq 2$. As a consequence, there are only trivial smooth time changes for these actions (up to an automorphism)

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