We study conformal deformations of a uniform space that satisfies the Ahlfors -regularity condition on balls of Whitney type. We verify the Gehring–Hayman Theorem by using a Whitney covering of the space.
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Pekka Koskela, Päivi Lammi, Gehring–Hayman Theorem for conformal deformations. Comment. Math. Helv. 88 (2013), no. 1, pp. 185–203DOI 10.4171/CMH/282