June 2021 An optimization problem arising in CR geometry
John P. D’Angelo
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Illinois J. Math. 65(2): 475-498 (June 2021). DOI: 10.1215/00192082-8947202

Abstract

We determine the asymptotic behavior as the degree tends to infinity of the minimal L1 norm m(n,d) of the solution of an optimization problem arising when studying polynomial sphere maps. Here n is the source dimension and d is the degree. We provide upper and lower bounds for m(n,d). We use these bounds to show that the function dm(n,d) is monotone increasing in d. We prove that limdm(n,d)d=n(n1). Let N(n,d) denote the minimum possible target dimension of a monomial sphere map of degree d. We show, in source dimension unequal to 2, that limdm(n,d)N(n,d)=n. The limit is 4 when n=2. We discuss some complicated results obtained by coding when n=2.

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John P. D’Angelo. "An optimization problem arising in CR geometry." Illinois J. Math. 65 (2) 475 - 498, June 2021. https://doi.org/10.1215/00192082-8947202

Information

Received: 20 July 2020; Revised: 12 November 2020; Published: June 2021
First available in Project Euclid: 25 March 2021

Digital Object Identifier: 10.1215/00192082-8947202

Subjects:
Primary: 32H35
Secondary: 32M99 , 32V99 , 90C05

Rights: Copyright © 2021 by the University of Illinois at Urbana–Champaign

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Vol.65 • No. 2 • June 2021
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