Decoupling for smooth surfaces in $\mathbb{R}^3$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866916461552861184 |
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| author | Li, Jianhui Yang, Tongou |
| author_facet | Li, Jianhui Yang, Tongou |
| contents | For each $d\geq 0$, we prove decoupling inequalities in $\mathbb R^3$ for the graphs of all bivariate polynomials of degree at most $d$ with bounded coefficients, with the decoupling constant depending uniformly in $d$ but not the coefficients of each individual polynomial. As a consequence, we prove a decoupling inequality for (a compact piece of) every smooth surface in $\mathbb{R}^3$, which in particular solves a conjecture of Bourgain, Demeter and Kemp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_08441 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Decoupling for smooth surfaces in $\mathbb{R}^3$ Li, Jianhui Yang, Tongou Classical Analysis and ODEs 42B99 (Primary), 53A05 (Secondary) For each $d\geq 0$, we prove decoupling inequalities in $\mathbb R^3$ for the graphs of all bivariate polynomials of degree at most $d$ with bounded coefficients, with the decoupling constant depending uniformly in $d$ but not the coefficients of each individual polynomial. As a consequence, we prove a decoupling inequality for (a compact piece of) every smooth surface in $\mathbb{R}^3$, which in particular solves a conjecture of Bourgain, Demeter and Kemp. |
| title | Decoupling for smooth surfaces in $\mathbb{R}^3$ |
| topic | Classical Analysis and ODEs 42B99 (Primary), 53A05 (Secondary) |
| url | https://arxiv.org/abs/2110.08441 |