2013/03/14 by G. P. Balakumar, Balakumar, G. P., Prachi Mahajan +3 · 1 citation
Mathematics · #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Primary 32F45 #Secondary 32Q45
paper · pdf · doi:10.48550/arxiv.1303.3439
openalex publication_date 2013/03/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Let D ⊂ ℂn be a smoothly bounded pseudoconvex Levi corank one domain with defining function r, i.e., the Levi form ∂ ∂ r of the boundary ∂ D has at least (n - 2) positive eigenvalues everywhere on ∂ D. The main goal of this article is to obtain a lower bound for the Carathéodory, Kobayashi and the Bergman distance between a given pair of points p, q ∈ D in terms of parameters that reflect the Levi geometry of ∂ D and the distance of these points to the boundary. Applications include an understanding of Fridman's invariant for the Kobayashi metric on Levi corank one domains, a description of the balls in the Kobayashi metric on such domains that are centered at points close to the boundary in terms of Euclidean data and the boundary behaviour of Kobayashi isometries from such domains.