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- W2020538862 abstract "Let ɛ be the family of all continua E in $$bar Ubackslash left{ 0 right}$$ , where U={¦z¦ < 1}, let U(E) be the connected component of UE containing the point z=0, let wE(z0=w(z0, E, U(E)) be the harmonic measure of E relative to the domain U(E) at the point z0 ∃ U(E). In the paper one answers affirmatively a question raised by B. Rodkin [K. F. Barth, D. A. Branna, and W. K. Hayman, “Research problems in complx analysis,” Bull. London Math. Soc.,l6, No. 5, 490–517, 1984]. Namely, one proves that in the family ɛ(d0) of continua E ∃ ɛ, satisfying the condition diam E=d0,o<d0⩽2, one has the inequality $$omega _{rm E} (0) geqslant frac{1}{pi }$$ arcsin d0/2, one indicates all the cases for which equality prevails." @default.
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- W2020538862 date "1987-08-01" @default.
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- W2020538862 title "Harmonic measure of continua with a fixed diameter" @default.
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- W2020538862 doi "https://doi.org/10.1007/bf01474448" @default.
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