@article{a33b7370d530460d8204b72b995523ec,
title = "Kummer rigidity for K3 surface automorphisms via RICCI-Flat metrics",
abstract = "We give an alternative proof of a result of Cantat & Dupont, showing that any automorphism of a K3 surface with measure of maximal entropy in the Lebesgue class must be a Kummer example. Our method exploits the existence of Ricci-flat metrics on K3s and also covers the non-projective case.",
author = "Simion Filip and Valentino Tosatti",
note = "Funding Information: Manuscript received September 28, 2018; revised November 15, 2019. Research supported by NSF grants DMS-1638352, DMS-1610278, DMS-2005470, and DMS-1903147; research of the first author supported by the Institute for Advanced Study and the Clay Mathematics Institute. American Journal of Mathematics 143 (2021), 1431–1462. {\textcopyright} 2021 by Johns Hopkins University Press. Funding Information: Acknowledgments. We would like to thank Alex Eskin, Carlos Matheus, Federico Rodriguez-Hertz, and Amie Wilkinson for discussions, Mattias Jonsson for useful comments on an earlier draft, and Serge Cantat, Curt McMullen and the referee for extensive feedback that significantly improved the exposition. This research was partially conducted during the period the first author served as a Clay Research Fellow, and during the second author{\textquoteright}s visits to the Center for Mathematical Sciences and Applications at Harvard University and to the Institut Henri Poincar{\'e} in Paris (supported by a Chaire Poincar{\'e} funded by the Clay Mathematics Institute) which he would like to thank for the hospitality and support. Publisher Copyright: {\textcopyright} 2021 by Johns Hopkins University Press.",
year = "2021",
month = oct,
doi = "10.1353/ajm.2021.0036",
language = "English (US)",
volume = "143",
pages = "1431--1462",
journal = "American Journal of Mathematics",
issn = "0002-9327",
publisher = "Johns Hopkins University Press",
number = "5",
}