6 papers
Cubic moments of eigenfunctions on surfaces
Xing Wang, Cheng Zhang
We identify Gaussian curvature as a local mechanism for cubic cancellation of Laplace eigenfunctions on Riemannian surfaces, without arithmetic or dynamical assumptions. For -…
-Logvinenko-Sereda sets and -Carleson measures on compact manifolds
Xing Wang, Xiangjin Xu, Cheng Zhang
Marzo and Ortega-Cerdà gave geometric characterizations for -Logvinenko-Sereda sets on the standard sphere for all . Later, Ortega-Cerdà and Pridhnani further i…
Strichartz estimates for orthonormal systems on compact manifolds
Xing Wang, An Zhang, Cheng Zhang
We establish new Strichartz estimates for orthonormal systems on compact Riemannian manifolds in the case of wave, Klein-Gordon and fractional Schrödinger equations. Our results ge…
A few sharp estimates of harmonic functions with applications to Steklov eigenfunctions
Xing Wang, Cheng Zhang
On smooth compact manifolds with smooth boundary, we first establish the sharp lower bounds for the restrictions of harmonic functions in terms of their frequency functions, by usi…
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…
Restriction of Schrödinger eigenfunctions to submanifolds
Xiaoqi Huang, Xing Wang, Cheng Zhang
For Schrödinger operators with critically singular potentials on compact manifolds, we prove sharp estimates for the restriction of eigenfunctions to submanifolds.…