Firstly, we pursue the work of W. Cherry on the analogue of the Kobayashi semidistance , which he introduced for analytic spaces defined over a non-Archimedean metrized field . We prove various characterizations of smooth projective varieties for which is an actual distance.
Secondly, we explore several notions of hyperbolicity for a smooth algebraic curve defined over . We prove a non-Archimedean analogue of the equivalence between having a negative Euler characteristic and the normality of certain families of analytic maps taking values in .
"Hyperbolicity Notions for Varieties Defined over a Non-Archimedean Field." Michigan Math. J. 69 (1) 41 - 78, March 2020. https://doi.org/10.1307/mmj/1574326880