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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.17107 |
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| _version_ | 1866914813466116096 |
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| author | Murdza, Andrew Nguyen, Khai T. |
| author_facet | Murdza, Andrew Nguyen, Khai T. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17107 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A sharp quantitative estimate of critical sets Murdza, Andrew Nguyen, Khai T. Functional Analysis 46T20 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. |
| title | A sharp quantitative estimate of critical sets |
| topic | Functional Analysis 46T20 |
| url | https://arxiv.org/abs/2405.17107 |