Subelliptic estimates of polynomial differential operators and applications to rigidity of abelian actions (Q1901648)

The authors 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. This is actually related to the maximal hypoellipticity of a family of generalized Laplacians of the type \(\sum_j X^{2m}_j\) where the real vector fields \(X_j\) satisfy Hörmander's well known condition. This property is used to extend the cocycle trivialization theorem for Anosov actions of higher rank Abelian groups [the authors, Publ. Math., Inst. Hautes Étud. Sci. 79, 131-156 (1994; Zbl 0819.58027)] to certain partially hyperbolic actions of \(\mathbb{Z}^k\) or \(\mathbb{R}^k\) \((k \geq 2)\). As a consequence, the authors get that there are only trivial smooth time changes for these actions (up to an automorphism).