Xiaoqi Huang

activity

20192026

most citedRestriction of toral eigenfunctions to totally geodesic submanifolds

7 citations · 18 across the 20 of their papers we have counts for

collaborators

21 papers

math.AP2026

Inhomogeneous Strichartz estimates on manifolds with nonpositive curvature and applications

Xiaoqi Huang, Connor Quinn

We prove lossless inhomogeneous Strichartz estimates for solutions to the Schrödinger equation on compact manifolds with nonpositive curvature over frequency-dependent time interva…

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.AP2024

Restriction of Schrödinger eigenfunctions to submanifolds

Xiaoqi Huang, Xing Wang, Cheng Zhang

For Schrödinger operators $H_{V} = - Δ_{g} + V$ with critically singular potentials $V$ on compact manifolds, we prove sharp estimates for the restriction of eigenfunctions to submanifolds.…

math.AP2024

Strichartz estimates for the Schrödinger equation on compact manifolds with nonpositive sectional curvature

Xiaoqi Huang, Christopher D. Sogge

We obtain improved Strichartz estimates for solutions of the Schrödinger equation on compact manifolds with nonpositive sectional curvatures which are related to the classical univ…

math.AP2024

Quasimode concentration on compact space forms

Xiaoqi Huang, Christopher D. Sogge

We show that the upper bounds for the $L^{2}$ -norms of $L^{1}$ -normalized quasimodes that we obtained in [9] are always sharp on any compact space form. This allows us to characterize…

math.AP2024

Curvature and sharp growth rates of log-quasimodes on compact manifolds

Xiaoqi Huang, Christopher D. Sogge

We obtain new optimal estimates for the $L^{2} (M) \to L^{q} (M)$ , $q \in (2, q_{c}]$ , $q_{c} = 2 (n + 1) / (n - 1)$ , operator norms of spectral projection operators associated with spectral windows $[λ…

math.AP2023

Strichartz estimates for the Schrödinger equation on negatively curved compact manifolds

Matthew D. Blair, Xiaoqi Huang, Christopher D. Sogge

We obtain improved Strichartz estimates for solutions of the Schrödinger equation on negatively curved compact manifolds which improve the classical universal results results of Bu…

math.AP2022

Sharp $L^{p}$ estimates and size of nodal sets for generalized Steklov eigenfunctions

Xiaoqi Huang, Yannick Sire, Xing Wang +1

We prove sharp $L^{p}$ estimates for the Steklov eigenfunctions on compact manifolds with boundary in terms of their $L^{2}$ norms on the boundary. We prove it by establishing $L^{p}$ bo…

math.AP2022★ 1 cited

Improved spectral projection estimates

Matthew D. Blair, Xiaoqi Huang, Christopher D. Sogge

We obtain new improved spectral projection estimates on manifolds of non-positive curvature, including sharp ones for relatively large spectral windows for general tori. Our result…

math.AP2022

Global uniform in $N$ estimates for solutions of a system of Hartree-Fock-Bogoliubov type in the Gross-Pitaveskii regime

Xiaoqi Huang

We extend the recent work of Chong et al., (2022) to the critical case. More precisely, we prove global in time, uniform in $N$ estimates for the solutions $ϕ$ , $Λ$ and $Γ$ of a co…

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★ 3 cited

Sharp Pointwise Weyl Laws for Schrödinger Operators with Singular Potentials on Flat Tori

Xiaoqi Huang, Cheng Zhang

The Weyl law of the Laplacian on the flat torus $T^{n}$ is concerning the number of eigenvalues $\leq λ^{2}$ , which is equivalent to counting the lattice points inside the ball…

math.AP2021

Pointwise Weyl Laws for Schrödinger operators with singular potentials

Xiaoqi Huang, Cheng Zhang

We consider the Schrödinger operators $H_{V} = - Δ_{g} + V$ with singular potentials $V$ on general $n$ -dimensional Riemannian manifolds and study whether various forms of pointwise Weyl la…

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★ 3 cited

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

Uniform Sobolev Estimates on compact manifolds involving singular potentials

Matthew D. Blair, Xiaoqi Huang, Yannick Sire +1

We obtain generalizations of the uniform Sobolev inequalities of Kenig, Ruiz and the fourth author \cite{KRS} for Euclidean spaces and Dos Santos Ferreira, Kenig and Salo \cite{DKS…

math.AP2020★ 1 cited

Weyl formulae for Schrödinger operators with critically singular potentials

Xiaoqi Huang, Christopher D. Sogge

We obtain generalizations of classical versions of the Weyl formula involving Schrödinger operators $H_{V} = - Δ_{g} + V (x)$ on compact boundaryless Riemannian manifolds with critically sin…

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…

math.AP2019★ 2 cited

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

Xiaoqi Huang, Yannick Sire, Cheng Zhang

This paper is devoted to interior, i.e. away from the boundary, estimates for eigenfunctions of the fractional Laplacian in an Euclidean domain of $R^{d}$ .

math.AP2019★ 7 cited

Restriction of toral eigenfunctions to totally geodesic submanifolds

Xiaoqi Huang, Cheng Zhang

We estimate the $L^{2}$ norm of the restriction to a totally geodesic submanifold of the eigenfunctions of the Laplace-Beltrami operator on the standard flat torus $T^{d}$ , $d…

Inhomogeneous Strichartz estimates on manifolds with nonpositive curvature and applications

Weyl laws for Schrödinger operators on compact manifolds with boundary

Restriction of Schrödinger eigenfunctions to submanifolds

Strichartz estimates for the Schrödinger equation on compact manifolds with nonpositive sectional curvature

Quasimode concentration on compact space forms

Curvature and sharp growth rates of log-quasimodes on compact manifolds

Strichartz estimates for the Schrödinger equation on negatively curved compact manifolds

Sharp Lp estimates and size of nodal sets for generalized Steklov eigenfunctions

Improved spectral projection estimates

Global uniform in N estimates for solutions of a system of Hartree-Fock-Bogoliubov type in the Gross-Pitaveskii regime

Heat kernel estimate in a conical singular space

Product Manifolds with Improved Spectral Cluster and Weyl Remainder Estimates

Sharp Pointwise Weyl Laws for Schrödinger Operators with Singular Potentials on Flat Tori

Pointwise Weyl Laws for Schrödinger operators with singular potentials

Uniform Sobolev estimates in Rn involving singular potentials

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

Uniform Sobolev Estimates on compact manifolds involving singular potentials

Weyl formulae for Schrödinger operators with critically singular potentials

Lp eigenfunction bounds for fractional Schrödinger operators on manifolds

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

Restriction of toral eigenfunctions to totally geodesic submanifolds

Sharp $L^{p}$ estimates and size of nodal sets for generalized Steklov eigenfunctions

Global uniform in $N$ estimates for solutions of a system of Hartree-Fock-Bogoliubov type in the Gross-Pitaveskii regime

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

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