Research

Publications & Preprints

I have long been an admirer of Bernhard Riemann's mathematics and have delved into various branches of geometry, including complex geometry, sub-Riemannian geometry, probability, stochastic differential geometry, and information geometry.

Topic 1. Invariant metrics in Complex geometry [Brief explanation]

1. Non Measure-Hyperbolicity of K3 surfaces and Hilbert scheme of points on K3 surfaces (with D. R. Morrison), {arXiv}, 15pp (submitted).

2. Statistical Bergman geometry (with J. Yum), {arXiv}, 29pp (submitted).

3. Deformation of a Hyperbolic embedding into the Projective Toric Variety (with J. Yoo), {arXiv} , 30pp (submitted).

4. Equivalence of Invariant metrics via Bergman kernel on complete noncompact K\"ahler manifolds, (with K. Lee), Mathematische Annalen 10.1007/s00208-023-02735-2 (online) 31 pp. 

5. Non-existence of complete K\"ahler metric of negatively pinched holomorphic sectional curvature, Complex Analysis and its Synergies 10.1007/s40627-023-00119-5 9(2023), no.2, Paper No. 9, 6 pp.

6. Bergman metric on the symmetrized bidisc and its consequences, (with Y. Yuan), International Journal of Mathematics, 10.1142/S0129167X22500719, 33 (2022), no. 10-11, Paper No. 2250071, 16 pp. 

7. Comparing the Carath\'eodory pseudo-distance and the K\"ahler-Einstein distance on the complete Reinhardt domains, Asian Journal of Mathematics,  10.4310/AJM.2022.v26.n1.a2, 26(2022), no.1, 7 pp.

8. The Kobayashi–Royden metric on punctured spheres (with J. Qian), Forum Mathematicum, 10.1515/forum-2019-0297, 32 (2020), no. 4, 7 pp.

9. Invariant metrics on the complex ellipsoid, Journal of Geometric Analysis, 10.1007/s12220-019-00333-w, 31(2021), no.2, 16 pp. 

Topic 2. Probabilistic methods in Differential geometry

10. Probabilistic method to fundamental gap problems on the Sphere (with G. Wei, G. Yang), {arXiv}, 24pp (submitted).

11. The stochastic Schwarz lemma on Kahler manifolds by couplings and its applications (with M. Chae, M. Gordina, G. Yang) Journal of London Mathematical Society http://dx.doi.org/10.1112/jlms.12849 (2023) 23pp.

12. A note on first eigenvalue estimates by coupling methods in K\"ahler and quaternion K\"ahler manifolds, (with F. Baudoin and G. Yang), Electronic Communications in Probability, 10.1214/22-ECP452, 27 (2022), Paper No. 12, 8 pp.

13. Octonionic Brownian Windings, (with G. Yang), Journal of Theoretical Probability, 10.1007/s10959-021-01127-z, 35(2022), no.3, 17 pp.

Topic 3. sub-Riemannian geometry

14. Shapr weighted CR trace Sobolev inequalties (with Z. Yan), {arXiv}, 25pp.

15. Sub-Riemannian Geodesics on $SL(2,{R})$ (with Domenico D’Alessandro), ESAIM: Control, Optimisation and Calculus of Variation 10.1051/cocv/2022068, 28(2022), Paper No. 76, 30 pp.

16. The subelliptic heat kernel of octonionic anti-de sitter fibration, (with F. Baudoin), SIGMA, Symmetry, Integrability and Geometry: Methods and Applications, 10.3842/SIGMA.2021.014. 17(2021), Paper No. 014, 9 pp. 

17. The subelliptic heat kernel on the octonionic Hopf fibration (with F. Baudoin), Potential Analysis, 10.1007/s11118-020-09854-4, 55 (2021), no. 2, 17 pp. 

Topic 4. Geometric Analysis

18. Rigidity results with curvature conditions from Lichnerowicz Laplacian and applications (with Nguyen Thac Dung, Tran Quang Huy), {arXiv}, 20pp (submitted).

19. Vanishing results from Lichnerowicz Laplacian on complete K\"ahler manifolds and applications (with Nguyen Thac Dung), Journal of Mathematical Analysis and Applications, 10.1016/j.jmaa.2022.126602, 517(2023), no.1, Paper No. 126602, 15 pp. 

20. Diameter theorems on Kahler and quaternion Kahler manifolds under a positive curvature lower bound (with M. Gordina),  {arXiv}, 22pp.

Physics paper

21. (2nd author) Development of a high-speed impedance measurement system for dual-frequency (with H. Lee and others), Rev SCI Instrum, {Journal}