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A distance estimate on the boundary of a conformal deformation of the unit ball satisfying a Harnack inequality and the Gehring-Hayman property

A distance estimate on the boundary of a conformal deformation of the unit ball satisfying a Harnack inequality and the Gehring-Hayman property

We establish some bounds for the natural distance function on the boundary of such a conformal deformation of the unit ball B n , n ≥ 2, that satisfies a Harnack inequality and the condition of the Gehring-Hayman theorem.The construction is useful especially for those points for which the radial …