Continuity of capacity of a holomorphic motion

2020/04/11 by Ransford, Thomas, Younsi, Malik, Ai, Wen-hui
#31A15 #37F45 #Complex Variables (math.CV) #FOS: Mathematics #primary 30C85 #secondary 30C62

paper · doi:10.48550/arxiv.2004.05266

Abstract

We study the behavior of various set-functions under holomorphic motions. We show that, under such deformations, logarithmic capacity varies continuously, while analytic capacity may not.

Related

• Continuous analytic capacity and holomorphic motions
• On behaviour of holomorphically contractible systems under non-monotonic sequences of sets
• A new plurisubharmonic capacity and functions holomorphic along holomorphic vector fields
• Potential theory and boundary behavior in the Drury-Arveson space
• Capacities, Green function and Bergman functions