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arXiv · 2503.09253

Smooth Approximations of Quasispheres

Spencer Cattalani
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Abstract

We prove that every $n$-dimensional 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.

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Spencer Cattalani. 2025-03-12. Smooth Approximations of Quasispheres. https://arxiv.org/abs/2503.09253

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