On minimal Rolle's domains for complex polynomials

Abstract

Define a subset of the complex plane to be a Rolle's domain if it contains (at least) one critical point of every complex polynomial P such that P(-1)=P(1). Define a Rolle's domain to be minimal if no proper subset is a Rolle's domain. In this paper, we investigate minimal Rolle's domains.

4 pages, AMS-LaTeX, no figures. v2: corrected Theorem 1, and minor edits