A sharp bound for the degree of proper monomial mappings between balls

John P. D'Angelo*, Šimon Kos, Emily Riehl

*Corresponding author for this work

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

The authors prove that a proper monomial holomorphic mapping from the two-ball to the N-ball has degree at most 2N-3, and that this result is sharp. The authors first show that certain group-invariant polynomials (related to Lucas polynomials) achieve the bound. To establish the bound the authors introduce a graph-theoretic approach that requires determining the number of sinks in a directed graph associated with the quotient polynomial. The proof also relies on a result of the first author that expresses all proper polynomial holomorphic mappings between balls in terms of tensor products.

Original languageEnglish
Pages (from-to)581-593
Number of pages13
JournalJournal of Geometric Analysis
Volume13
Issue number4
DOIs
Publication statusPublished - 2003
Externally publishedYes

Keywords

  • Lucas polynomials
  • Proper holomorphic mappings
  • unit ball

Fingerprint Dive into the research topics of 'A sharp bound for the degree of proper monomial mappings between balls'. Together they form a unique fingerprint.

  • Cite this