Testing families of analytic discs in the unit ball

2021/07/18 by Luca Baracco, Baracco, Luca, Stefano Pinton +1
Mathematics · #32V25 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32V25

paper · pdf · doi:10.48550/arxiv.2107.08420

Comments are welcome

arxiv created 2021/07/18 · arxiv updated 2021/07/20

Abstract

Let a,b,c∈ ℂ² be three non collinear points such that their mutual joining complex lines do not intersect the unit ball \mathbbB² and such that the line through a and b is tangent to \mathbbB². Then the set of lines concurrent to a,b and c is a testing family for continuous functions on \mathbbS³. This improves a result by the authors and solves a case left open in the literature as described by Globevnik.

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