On the complexity of proper holomorphic mappings between balls

Abstract

We make several new contributions to the study of proper holomorphic mappings between balls. Our results include a degree estimate for rational proper maps, a new gap phenomenon for convex families of arbitrary proper maps, and an interesting result about inverse images.

19 pages, plain tex; improved exposition, added corollary to Theorem 1, strengthened Theorem 4

Cited by in corpus (7)

• Normal forms, Hermitian operators, and CR maps of spheres and hyperquadrics
• Homotopy equivalence for proper holomorphic mappings
• Hermitian symmetric polynomials and CR complexity
• Algebraic Levi-flat hypervarieties in complex projective space
• Rational sphere maps, linear programming, and compressed sensing
• Uniqueness of certain polynomials constant on a line
• Symmetries in CR complexity theory