4 papers
A new strong rigidity phenomenon for the Bergman metric
Peter Ebenfelt, John N. Treuer, Ming Xiao
We establish a new local-to-global rigidity phenomenon for the Bergman metric. Namely, under natural geometric hypotheses, a local conformal identification of Bergman metrics deter…
Domains with Bergman metrics of constant curvature and Bergman-negligible subsets
Peter Ebenfelt, John N. Treuer, Ming Xiao
Let be a bounded domain in . Suppose the holomorphic sectional curvature of its Bergman metric equals a negative constant . We show that is biholomorphic…
Bergman kernels over polarized Kähler manifolds, Bergman logarithmic flatness, and a question of Lu-Tian
Peter Ebenfelt, Ming Xiao, Hang Xu
Let be a complete Kähler manifold, and let be a positive line bundle inducing a Kähler metric on . We study two Bergman kernels in this setting: the Ber…
Local algebraicity and localization of the Bergman kernel on Stein spaces with finite type boundaries
Peter Ebenfelt, Soumya Ganguly, Ming Xiao
On a two dimensional Stein space with isolated, normal singularities, smooth finite type boundary, and locally algebraic Bergman kernel, we establish an estimate on the type of the…