Mathematics > Metric Geometry
[Submitted on 12 Mar 2025
(v1)
, last revised 8 Apr 2025 (this version, v2)]
Title: Smooth Approximations of Quasispheres
Title: 光滑逼近的拟球面
Abstract: We prove that every quasisphere is the Gromov-Hausdorff limit of a sequence of locally smooth uniform quasispheres. We also prove an analogous result in the bi-Lipschitz setting. This extends recent results of D. Ntalampekos from dimension 2 to arbitrary dimension. In the process, we replace the second half of his argument by a completely different, more efficient approach, which should be applicable to other problems.
Submission history
From: Spencer Cattalani [view email][v1] Wed, 12 Mar 2025 10:51:39 UTC (9 KB)
[v2] Tue, 8 Apr 2025 19:18:21 UTC (11 KB)
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