Continuous ω q -Plurisubharmonic Exhaustion Functions on Kähler Manifolds

Abstract

In this paper, we study continuous ωq-plurisubharmonic exhaustion functions. It is shown that if (M,ω) is a Kahler manifold and Ω⋐M is a relatively compact open subset such that there exists a smooth strictly plurisubharmonic function on M and for every a∈∂Ω, there exists a neighborhood Ua of a in M such that Ua∩Ω has a continuous ωq-plurisubharmonic exhaustion function then Ω has a continuous ωq-plurisubharmonic exhaustion function.