The cohomological equation for partially hyperbolic diffeomorphisms

Abstract

We establish a theory for the existence and regularity of solutions to the cohomological equation over an accessible, partially hyperbolic diffeomorphism. As a by-product of our techniques, we show that for $r>1$, any $C^r$ homogeneous, locally compact submanifold of a $C^r$ manifold is in fact a $C^r$ submanifold.

94 pages, 8 figures

References in corpus (1)

• A characterization of submanifolds by a homogeneity condition

Cited by in corpus (12)

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• Invariant distributions and cohomology for geodesic flows and higher cohomology of higher-rank Anosov actions
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• Exponential Mixing of Nilmanifold Automorphisms
• On the ergodic properties of time changes of partially hyperbolic homogeneous flows
• Relating boundary and interior solutions of the cohomological equation for cocycles by isometries of negatively curved spaces. The Livsic case
• Central Limit theorem and cohomological equation on homogeneous spaces
• Structure of accessibility classes
• Hyperbolization of cocycles by isometries of the euclidean space