Xiaoqi Huang

activity

20192024

most citedInterior estimates for the eigenfunctions of the fractional Laplacian on a bounded Euclidean domain

2 citations · 3 across the 5 of their papers we have counts for

collaborators

7 papers

math.AP2024

Weyl laws for Schrödinger operators on compact manifolds with boundary

Xiaoqi Huang, Xing Wang, Cheng Zhang

We prove Weyl laws for Schrödinger operators with critically singular potentials on compact manifolds with boundary. We also improve the Weyl remainder estimates under the conditio…

math.AP2022

Heat kernel estimate in a conical singular space

Xiaoqi Huang, Junyong Zhang

Let $(X, g)$ be a product cone with the metric $g = d r^{2} + r^{2} h$ , where $X = C (Y) = (0, \infty)_{r} \times Y$ and the cross section $Y$ is a $(n - 1)$ -dimensional closed Riemannian manifold $(Y,h…

math.AP2022

Product Manifolds with Improved Spectral Cluster and Weyl Remainder Estimates

Xiaoqi Huang, Christopher D. Sogge, Michael E. Taylor

We show that if $Y$ is a compact Riemannian manifold with improved $L^{q}$ eigenfunction estimates then, at least for large enough exponents, one always obtains improved $L^{q}$ bounds…

math.AP2021★ 1 cited

Uniform Sobolev estimates in $R^{n}$ involving singular potentials

Xiaoqi Huang, Christopher D. Sogge

We generalize the Stein-Tomas [17] $L^{2}$ -restricition theorem and the uniform Sobolev estimates of Kenig, Ruiz and the second author [11] by allowing critically singular potential.…

math.AP2020

Quasimode and Strichartz estimates for time-dependent Schrödinger equations with singular potentials

Xiaoqi Huang, Christopher D. Sogge

We generalize the Strichartz estimates for Schrödinger operators on compact manifolds of Burq, Gérard and Tzvetkov [10] by allowing critically singular potentials $V$ . Specifically…

math.AP2020

$L^{p}$ eigenfunction bounds for fractional Schrödinger operators on manifolds

Xiaoqi Huang, Yannick Sire, Cheng Zhang

This paper is dedicated to $L^{p}$ bounds on eigenfunctions of a Schödinger-type operator $(- Δ_{g})^{α /2} + V$ on closed Riemannian manifolds for critically singular potentials $V$ . The…