Holomorphic maps on with attracting hypersurfaces and pluricomplex Green functions for their repellers

Abstract

The conditions under which a holomorphic endomorphism of a complex projective space has an attracting hypersurface are given. These are formulated in terms of estimates for plurisubharmonic exhaustions on the complement of the hypersurface, and estimates for pluricomplex Green functions of relatively compact sets. These conditions are applied to prove results about convergence of pluricomplex Green functions.

†To the memory of Yue Lin Lawrence Tong.

Keywords:

• Pluricomplex Green function
• Plurisubharmonic exhaustion
• Attractors

Keywords:

• 1991 Mathematics Subject Classifications: Primary: 32U10
• Secondary: 32U35
• 37B25
• 37F10

Notes

†To the memory of Yue Lin Lawrence Tong.