28 research outputs found
On the Bergman representative coordinates
We study the set where the so-called Bergman representative coordinates (or
Bergman functions) form an immersion. We provide an estimate of the size of a
maximal geodesic ball with respect to the Bergman metric, contained in this
set. By concrete examples we show that these estimates are the best possible.Comment: 20 page
Mixed Hessian inequalities and uniqueness in the class E(X,ω,m)
We prove a general inequality for mixed Hessian measures by global arguments. Our method also yields a simplification for the case of complex Monge–Ampère equation. Exploiting this and using Kołodziej’s mass concentration technique we also prove the uniqueness of the solutions to the complex Hessian equation on compact Kähler manifolds in the case of probability measures vanishing on (Formula presented.)-polar sets