Uniform perfectness of the Berkovich Julia sets in non-archimedean dynamics

Abstract

We show that a rational function $f$ of degree $>1$ on the projective line over an algebraically closed field that is complete with respect to a non-trivial and non-archimedean absolute value has no potentially good reductions if and only if the Berkovich Julia set of $f$ is uniformly perfect. As an application, a uniform regularity of the boundary of each Berkovich Fatou component of $f$ is also established.