Some Recent Results on the Geometry of Complex Polynomials: The\n Gauss--Lucas Theorem, Polynomial Lemniscates, Shape Analysis, and Conformal\n Equivalence

2019/10/02 by Trevor Richards, Trevor J. Richards, Richards, Trevor J.
Mathematics · Physics and Astronomy · #30C15 #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Algebra over a field #Complex Variables (math.CV) #Complex quadratic polynomial #Conformal field theory #Conformal geometry #Conformal map #Difference polynomials #Equivalence (formal languages) #FOS: Mathematics #Gauss #Geometry #Mathematical analysis #Mathematics #Mathematics and Applications #Orthogonal polynomials #Physics #Polynomial #Pure mathematics #math.CV #msc:30C15

paper · pdf · doi:10.48550/arxiv.1910.01159

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2019/10/02 · arxiv created 2020/01/11 · arxiv updated 2020/01/14 · openalex created_date 2022/07/28 · openalex updated_date 2026/08/06

Abstract

In this article, we survey the the recent literature surrounding the geometry\nof complex polynomials. Specific areas surveyed are i) Generalizations of the\nGauss--Lucas Theorem, ii) Geometry of Polynomials Level Sets, and iii) Shape\nAnalysis and Conformal Equivalence.\n

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