# American Institute of Mathematical Sciences

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Einstein-Lichnerowicz type singular perturbations of critical nonlinear elliptic equations in dimension 3
doi: 10.3934/dcds.2021044

## Centralizers of partially hyperbolic diffeomorphisms in dimension 3

 1 Queen's University, Kingston, Ontario 2 Ohio State University, Columbus, Ohio

* Corresponding author: Andrey Gogolev

Received  January 2021 Revised  January 2021 Published  March 2021

Fund Project: The first author was partially supported by the NSERC (Funding reference number RGPIN-2017-04592). The second author was partially supported by NSF DMS-1823150

In this note we describe centralizers of volume preserving partially hyperbolic diffeomorphisms which are homotopic to identity on Seifert fibered and hyperbolic 3-manifolds. Our proof follows the strategy of Damjanovic, Wilkinson and Xu [10] who recently classified the centralizer for perturbations of time-$1$ maps of geodesic flows in negative curvature. We strongly rely on recent classification results in dimension 3 established in [5,6].

Citation: Thomas Barthelmé, Andrey Gogolev. Centralizers of partially hyperbolic diffeomorphisms in dimension 3. Discrete & Continuous Dynamical Systems, doi: 10.3934/dcds.2021044
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