Yakun Xi

activity

20152024

most citedImproved critical eigenfunction restriction estimates on Riemannian surfaces with nonpositive curvature

12 citations · 63 across the 20 of their papers we have counts for

collaborators

Showing math.CAShow all

5 papers · 1 filter

math.CA2019

On Convexity, Mid-Point Convexity and Hausdorff Measures of Sets

Shaoming Guo, Tian Lan, Yakun Xi

We give a complete characterization of the size of Borel sets that are mid-point convex but not (essentially) convex, in terms of their Hausdorff dimensions and Hausdorff measures.

math.CA2019★ 9 cited

Microlocal decoupling inequalities and the distance problem on Riemannian manifolds

Alex Iosevich, Bochen Liu, Yakun Xi

We study the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the result of Guth-Iosevich-Ou-Wang for the distance set in the pla…

math.CA2018★ 11 cited

$ℓ^{2}$ Decoupling in $R^{2}$ for curves with Vanishing Curvature

Chandan Biswas, Maxim Gilula, Linhan Li +2

We expand the class of curves $(φ_{1} (t), φ_{2} (t)), t \in [0, 1]$ for which the $ℓ^{2}$ decoupling conjecture holds for $2 \leq p \leq 6$ . Our class of curves includes all real-analytic r…

math.CA2017★ 4 cited

On Instability of the Nikodym Maximal Function bounds over Riemannian Manifolds

Christopher D. Sogge, Yakun Xi, Hang Xu

We show that, for odd $d$ , the $L^{\frac{d + 2}{2}}$ bounds of Sogge and Xi for the Nikodym maximal function over manifolds of constant sectional curvature, are unstable with respect t…

math.CA2015★ 3 cited

On Kakeya-Nikodym type maximal inequalities