Fourier dimension of Mandelbrot Cascades on planar curves
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918411236278272 |
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| author | Ryou, Donggeun Suomala, Ville |
| author_facet | Ryou, Donggeun Suomala, Ville |
| contents | We consider multifractal Mandelbrot cascades supported on planar $C^2$ curves with nonvanishing curvature and show that their Fourier dimension is as large as possible, i.e., equal to the infimum of the lower pointwise dimension of the measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25615 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fourier dimension of Mandelbrot Cascades on planar curves Ryou, Donggeun Suomala, Ville Probability Mathematical Physics Classical Analysis and ODEs We consider multifractal Mandelbrot cascades supported on planar $C^2$ curves with nonvanishing curvature and show that their Fourier dimension is as large as possible, i.e., equal to the infimum of the lower pointwise dimension of the measure. |
| title | Fourier dimension of Mandelbrot Cascades on planar curves |
| topic | Probability Mathematical Physics Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2603.25615 |