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arXiv 0709.07952007-09-06math.MGmath.CV

曲面上的拟对称结构

Quasisymmetric structures on surfaces

Kevin Wildrick

备注：: 34 pages, 7 figures

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摘要：

我们证明了局部Ahlfors 2-正则和局部线性局部可收缩度量曲面与圆盘是局部拟对称等价的。我们还讨论了这个结果的应用问题的特征曲面在某些欧几里得空间是局部双Lipschitz等价的一个开子集的平面。

英文摘要：

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 in some Euclidean space that are locally bi-Lipschitz equivalent to an open subset of the plane.

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