On the Bergman Metric near Exponentially Flat Infinite Type Boundary Points

2026/07/27 by Ravi Shankar Jaiswal
#math.CV

paper · pdf

Abstract

We prove that the Bergman metric of a (possibly unbounded) pseudoconvex domain with an exponentially flat infinite type boundary point cannot be Einstein. Our result provides further evidence in support of the Cheng--Yau conjecture beyond the finite type setting.

Citations

• On the Bergman metric of a pseudoconvex domain with a strongly pseudoconvex polyhedral boundary point
• Asymptotic behaviour of the Bergman invariant and Kobayashi metric on exponentially flat infinite type domains
• Kähler-Einstein Bergman metrics on pseudoconvex domains of dimension two
• Bergman-Einstein metrics on two-dimensional Stein spaces
• On the classification of normal Stein spaces and finite ball quotients with Bergman-Einstein metrics
• Bergman-Einstein metric on a Stein space with a strongly pseudoconvex boundary
• Algebraicity of the Bergman Kernel
• On the dimension of the Bergman space for some unbounded domains

Related

• On the Bergman metric of a pseudoconvex domain with a strongly pseudoconvex polyhedral boundary point
• Kähler-Einstein Bergman metrics on pseudoconvex domains of dimension two
• Lower bounds on the Bergman metric near points of infinite type
• Asymptotic behaviour of the Bergman invariant and Kobayashi metric on exponentially flat infinite type domains
• Boundary Behavior of the Bergman Metric