Remez-type inequalities in the complex plane (Q877181)

Let \(G\subset \mathbb C\) be a domain bounded by a Jordan curve without cusps. In the paper under review, the authors obtain a \textit{sharp} upper bound for the modulus of a complex polynomial at an arbitrary boundary point of \(G\). The authors' method of proof makes use of properties of Green functions, principles of symmetrization and the technique of moduli of families of curves together with some of their earlier estimates.