Proper holomorphic mappings, positivity conditions, and isometric imbedding

John P. D'Angelo

Research output: Contribution to journalArticlepeer-review


This article discusses in detail how the study of proper holomorphic rational mappings between balls in different dimensions relates to positivity conditions and to isometric imbedding of holomorphic bundles. The first chapter discusses rational proper mappings between balls; the second chapter discusses seven distinct positivity conditions for real-valued polynomials in several complex variables; the third chapter reveals how these issues relate to an isometric imbedding theorem for holomorphic vector bundles proved by the author and Catlin.

Original languageEnglish (US)
Pages (from-to)341-371
Number of pages31
JournalJournal of the Korean Mathematical Society
Issue number3
StatePublished - 2003
Externally publishedYes


  • CR mappings
  • Hermitian forms
  • Holomorphic line bundles
  • Isometric imbedding
  • Positivity conditions
  • Proper holomorphic mappings
  • Unit ball

ASJC Scopus subject areas

  • Mathematics(all)


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