Rooftop envelopes and residual plurisubharmonic functions
Tom 128 / 2022
Annales Polonici Mathematici 128 (2022), 159-191
MSC: Primary 32U15; Secondary 32U05, 32U35, 32W20.
DOI: 10.4064/ap210624-12-11
Opublikowany online: 14 March 2022
Streszczenie
Given a negative plurisubharmonic function $\phi $ in a bounded pseudoconvex domain of $\mathbb C^n$, we introduce and study its residual function $g_\phi $ determined by the asymptotic behavior of $\phi $ near its singularity points, both inside the domain and on its boundary. For certain choices of $\phi $, the function $g_\phi $ coincides with different versions of pluricomplex Green functions. The study is motivated by a problem on when two given plurisubharmonic functions can be connected by a plurisubharmonic geodesic.
