TL;DR
This paper proves a multivariate Gauss-Lucas theorem using a new convexity concept, extending previous results and applying to multivariate stable polynomials.
Contribution
It introduces a novel convexity notion and generalizes Gauss-Lucas theorems to multivariate cases with applications to stable polynomials.
Findings
Theorem established for multivariate Gauss-Lucas with new convexity.
Generalization of previous univariate results.
Applications demonstrated for multivariate stable polynomials.
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.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Probability and Statistical Research