Multivariate Gauss-Lucas Theorems

2012/03/29 by Marek Kanter, Kanter, Marek
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Complex Variables (math.CV) #FOS: Mathematics #Probability and Statistical Research #math.CV

paper · pdf · doi:10.48550/arxiv.1203.6426

arxiv created 2012/03/29 · openalex publication_date 2012/03/29 · arxiv updated 2012/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.

Related

• Gauss-Lucas Theorems for Entire Functions on CM
• On asymptotic Gauss-Lucas theorem
• The Lee‐Yang and Pólya‐Schur programs. II. Theory of stable polynomials and applications
• Multivariate stable polynomials: theory and applications
• Strengthening the Gauss-Lucas theorem for polynomials with Zeros in the interior of the convex hull