Rooftop envelopes and residual plurisubharmonic functions

Abstract

Given a negative plurisubharmonic function $\varphi$ in a bounded pseudoconvex domain of ${\mathbb{C}}^n$, we introduce and study its residual function $g_{\varphi }$ determined by the asymptotic behavior of $\varphi$ near its singularity points, both inside the domain and on its boundary. For certain choices of $\varphi$, the function $g_{\varphi }$ 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.

Final form. To appear in Ann. Polon. Math