Restriction estimates using decoupling theorems and two-ends Furstenberg inequalities
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910753902034944 |
|---|---|
| author | Wang, Hong Wu, Shukun |
| author_facet | Wang, Hong Wu, Shukun |
| contents | We propose to study the restriction conjecture using decoupling theorems and two-ends Furstenberg inequalities. Specifically, we pose a two-ends Furstenberg conjecture, which implies the restriction conjecture. As evidence, we prove this conjecture in the plane by using the Furstenberg set estimate. Moreover, we use this planar result to prove a restriction estimate for $p>22/7$ in three dimensions, which implies Wolff's $5/2$-hairbrush bound for Kakeya sets in $\mathbb{R}^3$. Our approach also makes improvements for the restriction conjecture in higher dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08871 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Restriction estimates using decoupling theorems and two-ends Furstenberg inequalities Wang, Hong Wu, Shukun Classical Analysis and ODEs Combinatorics Metric Geometry We propose to study the restriction conjecture using decoupling theorems and two-ends Furstenberg inequalities. Specifically, we pose a two-ends Furstenberg conjecture, which implies the restriction conjecture. As evidence, we prove this conjecture in the plane by using the Furstenberg set estimate. Moreover, we use this planar result to prove a restriction estimate for $p>22/7$ in three dimensions, which implies Wolff's $5/2$-hairbrush bound for Kakeya sets in $\mathbb{R}^3$. Our approach also makes improvements for the restriction conjecture in higher dimensions. |
| title | Restriction estimates using decoupling theorems and two-ends Furstenberg inequalities |
| topic | Classical Analysis and ODEs Combinatorics Metric Geometry |
| url | https://arxiv.org/abs/2411.08871 |