12 citations · 63 across the 20 of their papers we have counts for
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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…