  We study minimum sets of singular plurisubharmonic functions and their
relation to upper contact sets. In particular we develop an algorithm checking
when a naturally parametrized curve is such a minimum set. The case of Koch
curves is studied in detail. We also study the size of the set of upper
non-contact points. We show that this set is always of Lebesgue measure zero
thus answering an open problem in the viscosity approach to the complex
Monge-Amp\`ere equation. Finally, we prove that similarly to the case of convex
functions, strictly plurisubharmonic lower tests yield existence of upper tests
with a control on the opening.
