2 papers
math.CA2026
Sharp microlocal Kakeya--Nikodym estimates for eigenfunctions with applications
Chuanwei Gao, Shukun Wu, Yakun Xi
We extend the microlocal Kakeya--Nikodym bounds for eigenfunctions of Blair--Sogge to a larger range of exponents, which is optimal in all dimensions on general manifolds.…
math.CA2025
Curved Kakeya sets and Nikodym problems on manifolds
Chuanwei Gao, Diankun Liu, Yakun Xi
In this paper, we study curved Kakeya sets associated with phase functions satisfying Bourgain's condition. In particular, we show that the analysis of curved Kakeya sets arising f…