Comparison of two notions of subharmonicity on non-archimedean curves

Abstract

We show that a continuous function on the analytification of a smooth proper algebraic curve over a non-archimedean field is subharmonic in the sense of Thuillier if and only if it is psh, i.e. subharmonic in the sense of Chambert-Loir and Ducros. This equivalence implies that the property psh for continuous functions is stable under pullback with respect to morphisms of curves. Furthermore, we prove an analogue of the monotone regularization theorem on the analytification of $$\mathbb {P}^{1}$$ and Mumford curves using this equivalence.