12 citations · 63 across the 20 of their papers we have counts for
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Refined restriction estimate for eigenfunctions on Riemannian surfaces
Chuanwei Gao, Changxing Miao, Yakun Xi
We refine the restriction estimates for Laplace eigenfunctions on a Riemannian surface, originally established by Burq, Gérard, and Tzvetkov. First, we establish estimates fo…
Surfaces in which every point sounds the same
Feng Wang, Emmett L. Wyman, Yakun Xi
We address a maximally structured case of the question, "Can you hear your location on a manifold," posed in arXiv:2304.04659 for dimension . In short, we show that if a compact…
Can you hear your location on a manifold?
Emmett L. Wyman, Yakun Xi
We introduce a variation on Kac's question, "Can one hear the shape of a drum?" Instead of trying to identify a compact manifold and its metric via its Laplace--Beltrami spectrum,…
A two term Kuznecov sum formula
Emmett L. Wyman, Yakun Xi
The Kuznecov sum formula, proved by Zelditch in the Riemannian setting, is an asymptotic sum formula $$N(λ) := \sum_{λ_j \leq λ} \left| \int_H e_j \, dV_H \right|^2 = C_{H,M} λ^{\o…
Improved local smoothing estimate for the wave equation in higher dimensions
Chuanwei Gao, Bochen Liu, Changxing Miao +1
In this paper, we establish the sharp -broad estimate for a class of phase functions satisfying the homogeneous convex conditions. As an application, we obtain improved local sm…
Geodesic bi-angles and Fourier coefficients of restrictions of eigenfunctions
Emmett Wyman, Yakun Xi, Steve Zelditch
This article concerns joint asymptotics of Fourier coefficients of restrictions of Laplace eigenfunctions of a compact Riemannian manifold to a submanifold . We…
Fourier coefficients of restrictions of eigenfunctions
Emmett L. Wyman, Yakun Xi, Steve Zelditch
Let be an orthonormal basis of Laplace eigenfunctions of a compact Riemannian manifold . Let be a submanifold and let be an orthonormal bas…
Square function estimates and Local smoothing for Fourier Integral Operators
Chuanwei Gao, Bochen Liu, Changxing Miao +1
We prove a variable coefficient version of the square function estimate of Guth--Wang--Zhang. By a classical argument of Mockenhaupt--Seeger--Sogge, it implies the full range of sh…
Improved Generalized Periods Estimates Over Curves on Riemannian Surfaces with Nonpositive Curvature
Emmett L. Wyman, Yakun Xi
We show that on compact Riemann surfaces of nonpositive curvature, the generalized periods, i.e. the -th order Fourier coefficients of eigenfunctions over a closed smooth…
Improved Generalized Periods estimates on Riemannian Surfaces with Nonpositive Curvature
Yakun Xi
We show that on compact Riemann surfaces of negative curvature, the generalized periods, i.e. the -th order Fourier coefficient of eigenfunctions over a period geodesic $γ…
Inner product of eigenfunctions over curves and generalized periods for compact Riemannian surfaces
Yakun Xi
We show that for a smooth closed curve on a compact Riemannian surface without boundary, the inner product of two eigenfunctions and restricted to , $|\int e_λ\o…
An Endpoint Version of Uniform Sobolev Inequalities
Tianyi Ren, Yakun Xi, Cheng Zhang
We prove an endpoint version of the uniform Sobolev inequalities in Kenig-Ruiz-Sogge [8]. It was known that strong type inequalities no longer hold at the endpoints; however, we sh…
Geodesic period integrals of eigenfunctions on Riemannian surfaces and the Gauss-Bonnet Theorem
Christopher D. Sogge, Yakun Xi, Cheng Zhang
We use the Gauss-Bonnet theorem and the triangle comparison theorems of Rauch and Toponogov to show that on compact Riemann surfaces of negative curvature period integrals of eigen…
Improved critical eigenfunction restriction estimates on Riemannian surfaces with nonpositive curvature
Yakun Xi, Cheng Zhang
We show that one can obtain improved geodesic restriction estimates for eigenfunctions on compact Riemannian surfaces with nonpositive curvature. We achieve this by adapting…
Bilinear Kakeya-Nikodym averages of eigenfunctions on compact Riemannian surfaces
Changxing Miao, Christopher D. Sogge, Yakun Xi +1
We obtain an improvement of the bilinear estimates of Burq, Gérard and Tzvetkov in the spirit of the refined Kakeya-Nikodym estimates of Blair and the second author. We do this by…