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arXiv · 2301.00432

A lower bound on the quantitative version of the transversality theorem

Andrew Murdza·Khai T. Nguyen
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Abstract

The present paper studies a quantitative version of the transversality theorem. More precisely, given a continuous function $f\in \mathcal{C}([0,1]^d,\mathbb{R}^m)$ and a manifold $W\subset \mathbb{R}^m$ of dimension $p$, a sharpness result on the upper quantitative estimate of the $(d+p-m)$-dimensional Hausdorff measure of the set $\mathcal{Z}_{W}^{f}=\left\{x\in [0,1]^d: f(x)\in W\right\}$, which was achieved in [8], will be proved in terms of power functions.

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Andrew Murdza, Khai T. Nguyen. 2023-01-01. A lower bound on the quantitative version of the transversality theorem. https://arxiv.org/abs/2301.00432

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