  We introduce tropical skeletons for Berkovich spaces based on results of
Ducros. Then we study harmonic functions on good strictly analytic spaces over
a non-trivially valued non-Archimedean field. Chambert-Loir and Ducros
introduced bigraded sheaves of smooth real-valued differential forms on
Berkovich spaces by pulling back Lagerberg forms with respect to
tropicalization maps. We give a new approach in which we allow pullback by more
general harmonic tropicalizations to get a larger sheaf of differential forms
with essentially the same properties, but with a better cohomological behavior.
A crucial ingredient is that tropical varieties arising from harmonic
tropicalization maps are balanced.
