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arXiv · 2405.17107

A sharp quantitative estimate of critical sets

Andrew Murdza·Khai T. Nguyen
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Abstract

The paper establishes a sharp quantitative estimate for the $(d-1)$-Hausdorff measure of the critical set of $\mathcal{C}^1$ vector-valued functions on $\mathbb{R}^d$. Additionally, we prove that for a generic $\mathcal{C}^2$ function where ``generic" is understood in the topological sense of Baire category, the critical set has a locally finite $(d-1)$-Hausdorff measure.

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Andrew Murdza, Khai T. Nguyen. 2024-05-27. A sharp quantitative estimate of critical sets. https://arxiv.org/abs/2405.17107

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