I am currently focusing on the following areas: 

1) Global regularity of the solutions to inhomogeneous Cauchy-Riemann (aka. d-bar) equation. I am particularly interested in the H\"older and Sobolev estimates on various types of pseudoconvex domains. 

2) Unique continuation problems arising from real and complex analysis. 

3) Deformation theory of complex structures with boundary in complex manifold. 

4) Properties of Bergman kernel and Bergman metric on weakly pseudoconvex domains. 

Publications and Preprints

[12] A homotopy formula for a_q domains in complex manifold (with Xianghong Gong) 2025, submitted, arXiv, 

[11] Sobolev and H\"older estimates for the $dbar$ equation on pseudoconvex domains of finite type in $\mathbb C^2$, 2024, 

J. Math. Anal. Appl.  arXiv, Journal

[10] Global Newlander-Nirenberg theorem on domains with finite smooth boundary in complex manifolds (with Xianghong Gong), 2024, submitted, arXiv

[9] Sobolev differentiability properties of the logarithmic modulus of real analytic functions (with Ruixiang Zhang), 2022, 

J. Funct. Anal. arXiv, Journal

[8] A unique continuation property for $|dbar u| \leq V |u|$, 2024, Math. Scand. arXiv, Journal

[7] On 1/2 estimate for global Newlander-Nirenberg theorem, 2023, Math. Ann. arXiv, Journal

[6] Boundary regularity of Bergman kernel in Hölder space, 2022, Pac. J. Math. arXiv, Journal

[5] A Solution Operator for the d-bar equation in Sobolev Spaces of negative index (with Liding Yao), 2021,  

Trans.  Amer.  Math.  Soc. arXiv, Journal

[4] New estimates of Rychkov's universal extension operator for Lipschitz domains and some applications, (with Liding Yao) , 2021, 

Math. Nachr. arXiv, Journal

[3] Sobolev 1/2 estimates for the d-bar equation on strictly pseudoconvex domains with C^2 boundary (with Liding Yao) , 2021, 

Amer. J. Math. arXiv, Journal

[2] Oblique derivative boundary value problems on families of planar domains, Bulletin des Sciences Mathématiques, 2020, arXiv, Journal

[1] Weighted Sobolev L^{p} estimates for homotopy operators on strictly pseudoconvex domains with C^{2} boundary, 2019, J. Geom. Anal. arXiv, Journal

UCI Analysis Seminar:  https://www.math.uci.edu/seminar_list

Online Analysis Research Seminar (OARS):  https://sites.google.com/view/o-a-r-s

Rutgers Complex Analysis, Harmonic Analysis and Complex Geometry Seminar:  https://sites.google.com/view/rutgers-ca-seminar/schedule