Kahlerity of invariant metrics on pseudoconvex domain of dimension two

2025/08/27 by Wang, Lang
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.19992

Abstract

For a two dimensional bounded pseudoconvex domain of finite type, we prove uniformization theorems via Kahler-Kobayashi metric or Kahler-Carath\acuteeodory metric with quasi-finite geometry of order three. In particular, a pseudoconvex Reinhardt domain of finite type is the unit ball if and only if the Bergman metric is a scalar multiple of the Kobayashi metric or Carath\acuteeodory metric. Moreover, we establish a rigidity theorem concerning holomorphic sectional curvature of Bergman metric and Lu constant.

Citations

• Local Rigidity of the Bergman Metric and of the Kähler Carathéodory Metric
• Asymptotic characterizations of strong pseudoconvexity on pseudoconvex domains of finite type in ℂ²
• A metric analogue of Hartogs' theorem
• The geometry of domains with negatively pinched Kähler metrics
• Holomorphic curvature of Finsler metrics and complex geodesics

Related

• Some aspects of the Kobayashi and Carathéodory metrics on pseudoconvex domains
• On the Boundary Behaviour of Invariants and Curvatures of the Kobayashi--Fuks Metric in Strictly Pseudoconvex Domains
• Estimates of invariant metrics on pseudoconvex domains near boundaries with constant Levi ranks
• Kähler-Einstein Bergman metrics on pseudoconvex domains of dimension two
• On isometries of the Kobayashi and Carathéodory metrics