ON HYPERCONVEXITY AND TOWARDS BUNDLE-VALUED KERNEL ASYMPTOTICS ON LOCALLY PSEUDOCONVEX DOMAINS

Abstract

After recalling basic results on the L2 ¯∂-cohomology groups and known existence criteria for bounded plurisubharmonic exhaustion functions on locally pseudoconvex bounded domains, results on the Bergman kernel on hyperconvex domains will be reviewed. Then, on locally pseudoconvex domains with certain regularity constraints on the boundary, a result on the asymptotics of the Bergman kernel is proved without assuming the existence of plurisubharmonic exhaustion functions, as an application of the finite-dimensionality of L2 ¯∂-cohomology groups.