Automorphisms of compact Kähler manifolds with slow dynamics

Cantat, Serge; Paris-Romaskevich, Olga

doi:10.1090/tran/8229

Automorphisms of compact Kähler manifolds with slow dynamics
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Trans. Amer. Math. Soc. 374 (2021), 1351-1389 Request permission

Abstract:

We study automorphisms of compact Kähler manifolds having slow dynamics. Adapting Gromov’s classical argument, we give an upper bound on the polynomial entropy and study its possible values in dimensions $2$ and $3$. We prove that every automorphism with sublinear derivative growth is an isometry; a counter-example is given in the $C^{\infty }$ context, answering negatively a question of Artigue, Carrasco-Olivera, and Monteverde in [Acta Math. Hungar. 152 (2017), pp. 140–149] on polynomial entropy. We also study minimal automorphisms of surfaces with respect to the Zariski or euclidean topology.

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