  A hypercomplex manifold is a manifold equipped with a triple of complex
structures $I, J, K$ satisfying the quaternionic relations. We define a
quaternionic analogue of plurisubharmonic functions on hypercomplex manifolds,
and interpret these functions geometrically as potentials of HKT (hyperk\"ahler
with torsion) metrics, and prove a quaternionic analogue of A.D. Aleksandrov
and Chern-Levine-Nirenberg theorems.
