The Borel Map for Compact Subanalytic Subsets of Cm

Paulo D. Cordaro, Giuseppe Della Sala, Bernhard Lamel

Publications: Contribution to journalArticlePeer Reviewed

Abstract

We define, for a compact subset K of complex Euclidean space containing the origin, the so-called Borel map (at the origin). We discuss its properties in detail and state, in the case when K is subanalytic, two conjectures relating the injectivity and surjectivity of the Borel map with properties of the polynomial hull of K. We give strong evidence for the validity of the conjectures (e.g. the open mapping property) and show that they are true when K is convex.

Original languageEnglish
Article number172
JournalJournal of Geometric Analysis
Volume34
Issue number6
DOIs
Publication statusPublished - Jun 2024

Austrian Fields of Science 2012

  • 101002 Analysis
  • 101009 Geometry

Keywords

  • 32A38 (primary)
  • 35N10
  • Borel map
  • Convex sets
  • Fréchet algebras of functions
  • Open mapping property
  • Sub analytic sets

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