Abstract
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 language | English (US) |
|---|---|
| Pages (from-to) | 341-371 |
| Number of pages | 31 |
| Journal | Journal of the Korean Mathematical Society |
| Volume | 40 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2003 |
Keywords
- CR mappings
- Hermitian forms
- Holomorphic line bundles
- Isometric imbedding
- Positivity conditions
- Proper holomorphic mappings
- Unit ball
ASJC Scopus subject areas
- General Mathematics