Xiaoqi Huang

activity

20242026

collaborators

7 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 SchrÃ¶dinger equation on compact manifolds with nonpositive curvature over frequency-dependent time interv…

math.AP2025

Restriction of SchrÃ¶dinger eigenfunctions to submanifolds

Xiaoqi Huang, Xing Wang, Cheng Zhang

For SchrÃ¶dinger operators $H_{V} = - I^_{g} + V$ with critically singular potentials $V$ on compact manifolds, we prove sharp estimates for the restriction of eigenfunctions to submanifold…

math.AP2025

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 $[Î…

math.AP2024

Weyl laws for SchrÃ¶dinger operators on compact manifolds with boundary

Xiaoqi Huang, Xing Wang, Cheng Zhang

We prove Weyl laws for SchrÃ¶dinger operators with critically singular potentials on compact manifolds with boundary. We also improve the Weyl remainder estimates under the conditi…

math.AP2024

Strichartz estimates for the SchrÃ¶dinger equation on compact manifolds with nonpositive sectional curvature

Xiaoqi Huang, Christopher D. Sogge

We obtain improved Strichartz estimates for solutions of the SchrÃ¶dinger equation on compact manifolds with nonpositive sectional curvatures which are related to the classical uni…

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…