%0 Journal Article
%T Asymptotic properties of extremal K£¿hler metrics of Poincar¨¦ type
%A Hugues Auvray
%J Mathematics
%D 2013
%I arXiv
%X Consider a compact K\"ahler manifold X with a simple normal crossing divisor D, and define Poincar\'e type metrics on X\D as K\"ahler metrics on X\D with cusp singularities along D. We prove that the existence of a constant scalar curvature (resp. an extremal) Poincar\'e type K\"ahler metric on X\D implies the existence of a constant scalar curvature (resp. an extremal) K\"ahler metric, possibly of Poincar\'e type, on every component of D. We also show that when the divisor is smooth, the constant scalar curvature/extremal metric on X\D is asymptotically a product near the divisor.
%U http://arxiv.org/abs/1401.0123v1