Quasisymmetric structures on surfaces

Wildrick, Kevin

doi:10.1090/S0002-9947-09-04861-2

Quasisymmetric structures on surfaces
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Trans. Amer. Math. Soc. 362 (2010), 623-659 Request permission

Abstract:

We show that a locally Ahlfors $2$-regular and locally linearly locally contractible metric surface is locally quasisymmetrically equivalent to the disk. We also discuss an application of this result to the problem of characterizing surfaces embedded in some Euclidean spaces that are locally bi-Lipschitz equivalent to a ball in the plane.

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