Diankun Liu

collaborators

4 papers

math.CA2026

Restriction estimates for surfaces with negative curvature in $R^{3}$

Shaoming Guo, Diankun Liu, Yakun Xi

In $R^{3}$ , we prove that $L^{q} \to L^{p}$ restriction estimates associated with smooth surfaces with negative Gaussian curvature hold for all $p > \frac{22}{7}$ and $q'<\frac{p}{2…

math.CA2025

Restriction and Kakeya maximal estimates in $R^{4}$

Tainara Borges, Tiklung Chan, Mingfeng Chen +3

By combining the planebrush argument of Katz and Zahl \cite{katz21} with the decoupling-incidence method of Wang and Wu \cite{WangWu2024}, we derive new bounds for the Fourier rest…

math.CA2025

Curved Kakeya sets for generic phases in odd dimensions

Shaoming Guo, Diankun Liu, Yakun Xi

We show that for each odd integer $n \geq 3$ , there is an open dense subset of HÃ¶rmander phase functions in $R^{n}$ for which the associated curved Kakeya sets have Hausdorff…

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…

Restriction estimates for surfaces with negative curvature in R3

Restriction and Kakeya maximal estimates in R4

Curved Kakeya sets for generic phases in odd dimensions

Curved Kakeya sets and Nikodym problems on manifolds

Restriction estimates for surfaces with negative curvature in $R^{3}$

Restriction and Kakeya maximal estimates in $R^{4}$