Funding:

2022.01-2026.12: National Natural Science Foundation of China grant (No:12131011), participant, in-progress.

Publications (Last updated: June 2024)

Liu, B. (2024). Mixed-norm of orthogonal projections and analytic interpolation on dimensions of measures. Revista Matemática Iberoamericana, 40(2024), 827-858.

Gao, C., Liu, B., Miao, C., Xi, Y. (2023). Square function estimates and local smoothing for Fourier integral operators. Proceedings of the London Mathematical Society, 126(2023), 1923–1960.

Gao, C., Liu, B., Miao, C., Xi, Y. (2023). Improved local smoothing estimate for the wave equation in higher dimensions. Journal of Functional Analysis, 284(9), 109879.

Iosevich, A., Liu, B., Xi, Y. (2022). Microlocal decoupling inequalities and the distance problem on Riemannian manifolds. American Journal of Mathematics, 144(6), 1601-1639.

Iosevich, A., Lai, C.K., Liu, B., Wyman, E. (2022). Fourier frames for surface-carried measures. International Mathematics Research Notices, 2022(3), 1644-1665.

Liu, B. (2021). Periodic structure of translational multi-tilings in the plane. American Journal of Mathematics, 143(6), 1841-1862.

Lev, N., Liu, B. (2021). Spectrality of polytopes and equidecomposability by translations. International Mathematics Research Notices, 2021(18), 13867-13891.

Liu, B. (2020). On Hausdorff dimension of radial projections. Revista Matemática Iberoamericana, 37(4), 1307-1319.

Lai, C.K., Liu, B., Prince, H. (2021). Spectral properties of some unions of linear spaces. Journal of Functional Analysis, 280(11), 108985.

Liu, B. (2020). Hausdorff dimension of pinned distance sets and the L²-method. Proceedings of the American Mathematical Society, 148(1), 333-341.

Lev, N., Liu, B. (2019). Multi‐tiling and equidecomposability of polytopes by lattice translates. Bulletin of the London Mathematical Society, 51(6), 1079-1098.

Liu, B. (2019). Improvement on 2-chains inside thin subsets of Euclidean spaces. The Journal of Geometric Analysis, 29(4), 3520-3539.

Iosevich, A., Liu, B. (2019). Equilateral triangles in subsets of ℝ^d of large Hausdorff dimension. Israel Journal of Mathematics, 231(1), 123-137.

Liu, B. (2019). Group actions, the Mattila integral and applications. Proceedings of the American Mathematical Society, 147(6), 2503-2516.

Liu, B. (2019). An L²-identity and pinned distance problem. Geometric and Functional Analysis, 29(1), 283-294.

Iosevich, A., Liu, B. (2019). Pinned distance problem, slicing measures, and local smoothing estimates. Transactions of the American Mathematical Society, 371(6), 4459-4474.

Liu, B. (2017). Finite configurations contained in subsets of Euclidean spaces. University of Rochester. (Ph.D. Thesis)

Iosevich, A., Liu, B. (2015). Falconer distance problem, additive energy and Cartesian products. Annales Academiae Scientiarum Fennicae-Mathematica, 41(2), 579–585.

Greenleaf, A., Iosevich, A., Liu, B., Palsson, E. (2015). A group-theoretic viewpoint on Erdős–Falconer problems and the Mattila integral. Revista Matemática Iberoamericana, 31(3), 799-810.

Liu, B. (2014). On radii of spheres determined by subsets of Euclidean space. Journal of Fourier Analysis and Applications, 20(3), 668-678.