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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2304.12595 |
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| _version_ | 1866910335526502400 |
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| author | Cao, Zhenbin Miao, Changxing Wang, Zijian |
| author_facet | Cao, Zhenbin Miao, Changxing Wang, Zijian |
| contents | Fourier decay of fractal measures on surfaces plays an important role in geometric measure theory and partial differential equations. In this paper, we study the quadratic surfaces of high co-dimensions. Unlike the case of co-dimension 1, quadratic surfaces of high co-dimensions possess some special scaling structures and degenerate characteristics. We will adopt the strategy from Du and Zhang, combined with the broad-narrow analysis with different dimensions as divisions, to obtain a few lower bounds of Fourier decay of fractal measures on quadratic surfaces of co-dimension two in $\mathbb{R}^5$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_12595 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fourier decay of fractal measures on surfaces of co-dimension two in $\mathbb{R}^5$ Cao, Zhenbin Miao, Changxing Wang, Zijian Classical Analysis and ODEs Fourier decay of fractal measures on surfaces plays an important role in geometric measure theory and partial differential equations. In this paper, we study the quadratic surfaces of high co-dimensions. Unlike the case of co-dimension 1, quadratic surfaces of high co-dimensions possess some special scaling structures and degenerate characteristics. We will adopt the strategy from Du and Zhang, combined with the broad-narrow analysis with different dimensions as divisions, to obtain a few lower bounds of Fourier decay of fractal measures on quadratic surfaces of co-dimension two in $\mathbb{R}^5$. |
| title | Fourier decay of fractal measures on surfaces of co-dimension two in $\mathbb{R}^5$ |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2304.12595 |