The primary objective of this paper is to study core sets in the setting of
m-subharmonic functions on the class of (non-compact) Kahler manifolds. Core
sets are investigated in different aspects by considering various classes of
plurisubharmonic functions. One of the crucial concepts in studying the
structure of this kind of sets is the pseudoconcavity. In a more general way,
we will have the structure of core defined with respect to the m-subharmonic
functions, which we call m-core in our setting, in terms of m-pseudoconcave
sets. In the context of m-subharmonic functions, we define m-harmonic functions
and show that, in Cn,(n≥2) and more generally in any
Kahler manifold of dimension at least 2, m-harmonic functions are pluriharmonic
functions for m≥2.Comment: 11 page