Instytut Matematyczny Polskiej Akademii Nauk / pl / Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Wszystkie zeszyty

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.