تقرير
Bounds on the dimension of lineal extensions
| العنوان: | Bounds on the dimension of lineal extensions |
|---|---|
| المؤلفون: | Bushling, Ryan E. G., Fiedler, Jacob B. |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Classical Analysis and ODEs, 03D32, 28A80 (Primary) 68Q30 (Secondary) |
| الوصف: | Let $E \subseteq \mathbb{R}^n$ be a union of line segments and $F \subseteq \mathbb{R}^n$ the set obtained from $E$ by extending each line segment in $E$ to a full line. Keleti's line segment extension conjecture posits that the Hausdorff dimension of $F$ should equal that of $E$. Working in $\mathbb{R}^2$, we use effective methods to prove a strong packing dimension variant of this conjecture, from which the generalized Kakeya conjecture for packing dimension immediately follows. This is followed by several doubling estimates in higher dimensions and connections to related problems. Comment: 24 pages, 1 figure. Referee comments incorporated. Proof of Theorem 1.3 simplified. Several typos corrected |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2404.16315 |
| رقم الأكسشن: | edsarx.2404.16315 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |