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The highest smoothness of the Green function implies the highest density of a set

The highest smoothness of the Green function implies the highest density of a set

We investigate local properties of the Green function of the complement of a compact set EĻ…[0,1] with respect to the extended complex plane. We demonstrate, that if the Green function satisfies the 1/2-Hƶlder condition locally at the origin, then the density of E at 0, in terms of logarithmic capacity, ā€¦