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A quantitative version of strong localization of the Kobayashi, Azukawa and Sibony metrics, as well as of the squeezing function, near a plurisubharmonic peak boundary point of a domain in $Bbb C^n$ is given. As an application, the behavior of these metrics near a strictly pseudoconvex boundary point is studied. A weak localization of the three metrics and the squeezing function is also given near a plurisubharmonic antipeak boundary point.
Important geometric or analytic properties of domains in the Euclidean space $mathbb{R}^n$ or its one-point compactification (the Mobius space) $overline{mathbb{R}}^n$ $(nge 2)$ are often characterized by comparison inequalities between two intrinsic
We present a method for constructing global holomorphic peak functions from local holomorphic support functions for broad classes of unbounded domains. As an application, we establish a method for showing the positivity and completeness of invariant
We obtain explicit bounds on the difference between local and global Kobayashi distances in a domain of $mathbb C^n$ as the points go toward a boundary point with appropriate geometric properties. We use this for the global comparison of various inva
We consider Lie algebras admitting an ad-invariant metric, and we study the problem of uniqueness of the ad-invariant metric up to automorphisms. This is a common feature in low dimensions, as one can observe in the known classification of nilpotent
We summarize some work on CR mappings invariant under a subgroup of U(n) and prove a result on the failure of rigidity.