Mathematical Research Letters

Volume 1 (1994)

Number 2

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

Pages: 193 – 202

DOI: http://dx.doi.org/10.4310/MRL.1994.v1.n2.a7

Authors

A. Katok (Pennsylvania State University)

R. J. Spatzier (University of Michigan)

Abstract

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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