Publications & Preprints
Topic 1. Invariant metrics in Complex geometry [Brief explanation]
Non Measure-Hyperbolicity of K3 surfaces and Hilbert scheme of points on K3 surfaces (with D. R. Morrison), {arXiv}, 15pp (submitted) [Presentation note on 9/27/204 at Texas State Univ Topology seminar].
Deformation of a Hyperbolic embedding into the Projective Toric Variety (with J. Yoo), {arXiv} , 30pp, revising.
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.
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.
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.
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.
The Kobayashi–Royden metric on punctured spheres (with J. Qian), Forum Mathematicum, 10.1515/forum-2019-0297, 32 (2020), no. 4, 7 pp.
Invariant metrics on the complex ellipsoid, Journal of Geometric Analysis, 10.1007/s12220-019-00333-w, 31(2021), no.2, 16 pp.
Topic 2. Probability, Stochastic differential geometry, Information geometry, Schramm-Loewner Evolution
Statistical Bergman geometry (with J. Yum), {arXiv}, 41pp (submitted).
Probabilistic method to fundamental gap problems on the Sphere (with G. Wei, G. Yang), {arXiv}, Transactions of the American Mathematical Society (accepted).
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.
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.
Octonionic Brownian Windings, (with G. Yang), Journal of Theoretical Probability, 10.1007/s10959-021-01127-z, 35(2022), no.3, 17 pp.
Topic 3. Geometric analysis and sub-Riemannian geometry
Sharp lower bounds for the first eigenvalue of Steklov-type eigenvalue problems on a compact surface (with K. Seo), {arXiv}, 13pp.
Sharp weighted CR trace Sobolev inequalties (with Z. Yan), {arXiv}, 25pp.
Rigidity results with curvature conditions from Lichnerowicz Laplacian and applications (with Nguyen Thac Dung, Tran Quang Huy), {arXiv}, 26pp.
Diameter theorems on Kahler and quaternion Kahler manifolds under a positive curvature lower bound (with M. Gordina), {arXiv}, 22pp. Differential Geometry and Its Applications, https://doi.org/10.1016/j.difgeo.2024.102218.
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.
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.
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.
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.
Physics paper
(2nd author) Development of a high-speed impedance measurement system for dual-frequency (with H. Lee and others), Rev SCI Instrum, {Journal}