The stars at infinity in several complex variables

2023/02/24 by Anders Karlsson, Karlsson, Anders
Mathematics · Physics and Astronomy · #32F45 #32H40 (Secondary) #32H50 #32M18 #32Q15 #32Q45 (Primary) #Advanced Differential Geometry Research #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2302.12671

openalex publication_date 2023/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This text reviews certain notions in metric geometry that may have further applications to problems in complex geometry and holomorphic dynamics in several variables. The discussion contains a few unrecorded results and formulates a number of questions related to the asymptotic geometry and boundary estimates of bounded complex domains, boundary extensions of biholomorphisms, the dynamics of holomorphic self-maps, Teichmüller theory, and the existence of constant scalar curvature metrics on compact Kähler manifolds.

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