Visiting Assistant Professor
|Office||1019 Hylan Building|
|E-mail:||yxi4 at math dot rochester period edu|
- MW 5:00-6:00 pm
Courses I’m teaching this semester
Harmonic analysis: Kakeya-Nikodym problems, eigenfunction estimates.
Publications and Preprints
On Kakeya-Nikodym maximal inequalities, Transaction of American Mathematical Society 369 (2017), 6351-6372.
Bilinear Kakeya-Nikodym averages of eigenfunction on compact Riemannian surfaces, (with C. Miao, C. D. Sogge and J. Yang), Journal of Functional Analysis, (2016) 271: 2752.
Improved critical eigenfunction restriction estimates on Riemannian surfaces with nonpositive curvature, (with C. Zhang), Communications in Mathematical Physics, (2017) 350: 1299.
Geodesic period integrals of eigenfunctions on Riemannian surfaces and the Gauss-Bonnet Theorem, (with C. D. Sogge and C. Zhang), Cambridge Journal of Mathematics, (2017) 5: 123.
On instability of the Nikodym maximal function bounds over Riemannian manifolds, (with C. D. Sogge and H. Xu), Journal of Geometric Analysis, (2018) 28(3): 28862901..
An endpoint version of uniform resolvent estimate for the Laplacian, (with T. Ren and C. Zhang), to appear in Forum Mathematicum, (2018) 30(5): 1279-1289.
Inner product of eigenfunctions over curves and generalized periods for compact Riemannian surfaces, to appear in Journal of Geometric Analysis.
Improved generalized periods estimates on Riemannian surfaces with nonpositive curvature, preprint, arXiv:1711.09864.
Improved generalized periods estimates over curves on Riemannian surfaces with nonpositive curvature, (with E. Wyman), preprint, arXiv:1807.00041.
ℓ^2 Decoupling in ℝ^2 for curves with vanishing curvature, (with C. Biswas, M. Gilula, L. Li and J. Schwend), preprint, arXiv:1812.04760.