Remarks on the Gauss-Lucas theorem in higher dimensional space

Goodman, A. W.

doi:10.1090/S0002-9939-1976-0435366-6

Remarks on the Gauss-Lucas theorem in higher dimensional space

Author: A. W. Goodman
Journal: Proc. Amer. Math. Soc. 55 (1976), 97-102
MSC: Primary 30A08; Secondary 26A78
DOI: https://doi.org/10.1090/S0002-9939-1976-0435366-6
MathSciNet review: 0435366
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Abstract: A recent paper by J. B. Diaz and Dorothy Browne Shaffer extends the Gauss-Lucas Theorem to -dimensional Euclidean space. The authors leave open certain natural questions concerning the existence of ``zeros of the derivative". This paper answers three such questions, and suggests several other questions for further investigation.

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