The Borel Map for Compact Subanalytic Subsets of Cm
- Author(s)
- Paulo D. Cordaro, Giuseppe Della Sala, Bernhard Lamel
- 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.
- Organisation(s)
- Department of Mathematics
- External organisation(s)
- Instituto Oceanográfico, American University of Beirut
- Journal
- Journal of Geometric Analysis
- Volume
- 34
- ISSN
- 1050-6926
- DOI
- https://doi.org/10.1007/s12220-024-01596-8
- Publication date
- 06-2024
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 101002 Analysis, 101009 Geometry
- Keywords
- ASJC Scopus subject areas
- Geometry and Topology
- Portal url
- https://ucrisportal.univie.ac.at/en/publications/5261a935-31f3-4c95-ad59-87a55011c050