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

被引：1

作者：

John P. D’Angelo

Šimon Kos

Emily Riehl

机构：

[1] Department of Mathematics, University of Illinois, Urbana, IL 61801

[2] Center for Nonlinear Studies, Los Alamos National Laboratory, MS B258, Los Alamos

来源：

The Journal of Geometric Analysis | 2003年 / 13卷 / 4期

基金：

美国国家科学基金会;

关键词：

Lucas polynomials; Proper holomorphic mappings; unit ball;

D O I：

10.1007/BF02921879

中图分类号：

学科分类号：

摘要：

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. © 2003 Mathematica Josephina, Inc.

引用

页码：581 / 593

页数：12

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