Paper detail

The space of Poincaré type Kähler metrics on the complement of a divisor

Consider a divisor D with simple normal crossings in a compact Kähler manifold X. We show in this article that a Kähler metric in an arbitrary class, with constant scalar curvature and cusp singularities along the divisor is unique in this class when K[D] is ample. This we do by generalizing Chen's construction of approximate geodesics in the space of Kähler metrics, and proving an approximate version of the Calabi-Yau theorem, both independently of the ampleness of K[D].