My Mathematical Publications in Analysis and Geometry
On the Cauchy-Riemann Equation:
• Uniform estimates for the canonical solution to the ∂̄-equation on product domains (with Yifei Pan and Yuan Zhang), arXiv: 2006.14484, 25 pages.
• Sharp pointwise and uniform estimates for ∂̄ (with Song-Ying Li and John N. Treuer), Analysis & PDE 16-2 (2023), 407--431. MathSciNet, zbMATH, arXiv: 1911.12072
On Invariant Metrics:
• Bergman representative coordinate, constant holomorphic curvature and a multidimensional generalization of Carathéodory's theorem (with Bun Wong), arXiv:2209.08741, 26 pages. PDF
• Bergman-Calabi diastasis and Kähler metric of constant holomorphic sectional curvature (with Bun Wong), Pure and Applied Mathematics Quarterly (Special Issue in honor of Joseph J. Kohn) 18 (2022), 481--502. MathSciNet, zbMATH, arXiv: 2109.01282
On the Suita Conjecture:
• Rigidity Theorems by Capacities and Kernels (with John N. Treuer and Yuan Zhang), International Mathematics Research Notices, IMRN, Volume 2023, Issue 24, December 2023, Pages 21180--21214. arXiv: 2111.10973 (supersedes and generalizes arXiv: 2011.05273 and arXiv: 2101.01358)
• Rigidity Theorem by the Minimal Point of the Bergman Kernel (with John Treuer), The Journal of Geometric Analysis 31 (2021), 4856--4864. MathSciNet, zbMATH, arXiv: 2001.01856
• Equality in Suita's conjecture and metrics of constant Gaussian curvature, arXiv: 1807.05537, 22 pages. PDF
• Evans-Selberg potential on planar domains, Proceedings of the Japan Academy, Ser. A, Mathematical Sciences 93 (2017), 23--26. MathSciNet, zbMATH, arXiv: 1704.00137
• Suita Conjecture for a Punctured Torus, New Trends in Analysis and Interdisciplinary Applications, 199--206, Trends in Mathematics. Research Perspectives, Birkhäuser/Springer, Cham, 2017. MathSciNet, zbMATH, arXiv: 1603.09118
• Suita conjecture for a complex torus, Chinese Annals of Mathematics, Ser. A 35 (2014), 101--108 (in Chinese); translation in Chinese Journal of Contemporary Mathematics 35 (2014), 83--88. MathSciNet, zbMATH, arXiv: 1403.7447
On Bergman Kernels at Degeneration:
• Boundary asymptotics of the relative Bergman kernel metric for curves, Calculus of Variations and Partial Differential Equations 62:10 (2023), 1--29. MathSciNet, zbMATH, arXiv: 2005.11826
• Boundary Asymptotics of the Relative Bergman Kernel Metric for Elliptic Curves IV: Taylor Series, Geometric Complex Analysis, 129--143, Springer Proceedings in Mathematics & Statistics, Springer, Singapore, 2018. MathSciNet, zbMATH
• Boundary asymptotics of the relative Bergman kernel metric for hyperelliptic curves, Complex Manifolds 4 (2017), 7--15. MathSciNet, zbMATH
• Boundary asymptotics of the relative Bergman kernel metric for elliptic curves III: 1 & ∞, Journal of Classical Analysis 9 (2016), 61--67. MathSciNet, zbMATH
• Boundary asymptotics of the relative Bergman kernel metric for elliptic curves II: subleading terms, Annales Polonici Mathematici 118 (2016), 59--69. MathSciNet, zbMATH
• Boundary asymptotics of the relative Bergman kernel metric for elliptic curves, Comptes Rendus Mathématique. Académie des Sciences, Paris 353 (2015), 611--615. MathSciNet, zbMATH
Other Publication:
• Bergman kernel and its boundary asymptotics (ベルグマン核とその境界漸近性), PhD Thesis at Nagoya University, 27-Sep-2016.
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