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- W2059593657 abstract "A polygon PN is the unit disk ${Bbb D}$ with $n$ distinguished boundary points, $4le n le N$. An extremal quasiconformal mapping $f_0: {Bbb D}_zto {Bbb D}_w$ maps each polygon $P_N$ inscribed in ${Bbb D}_z$ onto a polygon $P_N'$ inscribed in ${Bbb D}_w$. Let fN be the extremal quasiconformal mapping of PN onto P'N. Let KN be its dilatation and let K0 be the maximal dilatation of f0. Then, evidently $sup K_Nle K_0$. The problem is, when equality holds. This is completely answered, if f0 does not have any essential boundary points. For quadrilaterals Q and Q' = f0(Q) the problem is sup(M'/M) = K0, with M and M' the moduli of Q and Q' respectively." @default.
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- W2059593657 date "1999-02-01" @default.
- W2059593657 modified "2023-09-23" @default.
- W2059593657 title "On the dilatation of extremal quasiconformal mappings of polygons" @default.
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- W2059593657 doi "https://doi.org/10.1007/s000140050080" @default.
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