# Faculty

## Yakun Xi

*Visiting Assistant Professor of Mathematics*

1019 Hylan Building

(585) 275-4419

Fax: (585) 273-4655

yxi4@math.rochester.edu

Office Hours: MW 3:30-4:30 p.m.

### Courses Taught

### Selected Publications

*On Convexity, Mid-Point Convexity and Hausdorff Measures of Sets*, (with S. Guo and T. Lan), preprint,**arXiv:1911.10032**.*Microlocal decoupling inequalities and the distance problem on Riemannian manifolds*, (with A. Iosevich and B. Liu), preprint,**arXiv:1909.05171**.*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**, to appear in**Proceedings of American Mathematical Society**.*Improved generalized periods estimates over curves on Riemannian surfaces with nonpositive curvature*, (with E. Wyman), preprint,**arXiv:1807.00041**.*Improved generalized periods estimates on Riemannian surfaces with nonpositive curvature*, preprint,**arXiv:1711.09864**.*Inner product of eigenfunctions over curves and generalized periods for compact Riemannian surfaces*, to appear in**Journal of Geometric Analysis**.*An endpoint version of uniform resolvent estimate for the Laplacian*, (with T. Ren and C. Zhang),**Forum Mathematicum, (2018) 30(5): 1279-1289**.*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**.*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**.*Improved critical eigenfunction restriction estimates on Riemannian surfaces with nonpositive curvature*, (with C. Zhang),**Communications in Mathematical Physics, (2017) 350: 1299**.*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**.*On Kakeya-Nikodym maximal inequalities*,**Transaction of American Mathematical Society 369 (2017), 6351-6372**.