Rooftop envelopes and residual plurisubharmonic functions

Abstract

Given a negative plurisubharmonic function φ in a bounded pseudoconvex domain of C, we introduce and study its residual function gφ determined by the asymptotic behavior of φ near its singularity points, both inside the domain and on its boundary. For certain choices of φ, the function gφ coincides with different versions of pluricomplex Green functions. The considerations are motivated by a problem on when two given plurisubharmonic functions can be connected by a plurisubharmonic geodesic. Mathematic Subject Classification: 32U05, 32U15, 32U35, 32W20