Four-point distortion theorem for complex polynomials

V. N. Dubinin

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arXiv · 1301.3985

Four-point distortion theorem for complex polynomials

V. N. Dubinin

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Abstract

We prove a theorem on distortion of cross ratio of four points under the mapping effected by a complex polynomial with restricted critical values. Its corollaries include inequalities involving the absolute value and certain coefficients of a polynomial. In particular, an exact lower bound is established for maximal moduli of critical values of polynomials $P$ of degree $n$ normalized by $P(0)=0$, $P'(0)\ne0$.

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V. N. Dubinin. 2013-01-17. Four-point distortion theorem for complex polynomials. https://arxiv.org/abs/1301.3985

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