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Spring 2012 Polynomials constant on a hyperplane and CR maps of spheres
Jiří Lebl, Han Peters
Illinois J. Math. 56(1): 155-175 (Spring 2012). DOI: 10.1215/ijm/1380287465

Abstract

We prove a sharp degree bound for polynomials constant on a hyperplane with a fixed number of nonnegative distinct monomials. This bound was conjectured by John P. D’Angelo, proved in two dimensions by D’Angelo, Kos and Riehl and in three dimensions by the authors. The current work builds upon these results to settle the conjecture in all dimensions. We also give a complete description of all polynomials in dimensions 4 and higher for which the sharp bound is obtained. The results prove the sharp degree bounds for monomial CR mappings of spheres in all dimensions.

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Jiří Lebl. Han Peters. "Polynomials constant on a hyperplane and CR maps of spheres." Illinois J. Math. 56 (1) 155 - 175, Spring 2012. https://doi.org/10.1215/ijm/1380287465

Information

Published: Spring 2012
First available in Project Euclid: 27 September 2013

zbMATH: 1278.14073
MathSciNet: MR3117023
Digital Object Identifier: 10.1215/ijm/1380287465

Subjects:
Primary: 05A20, 11C08, 14P99, 32H35

Rights: Copyright © 2012 University of Illinois at Urbana-Champaign

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Vol.56 • No. 1 • Spring 2012
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