Dr. Xin Dong's Publications
On the Cauchy-Riemann Equation:
• Uniform Estimates for the Canonical Solution to the ∂̄-equation on Product Domains (with Yifei Pan and Yuan Zhang), The Journal of Geometric Analysis, 35:121 (2025), 1--31. MathSciNet, zbMATH, arXiv:2006.14484
• 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 Holomorphically Invariant Metrics:
• Local Rigidity of the Bergman Metric and of the Kähler Carathéodory Metric (with Ruoyi Wang and Bun Wong), arXiv:2408.09572, 18 pages. PDF
• Bergman representative coordinate, constant holomorphic curvature and a multidimensional generalization of Carathéodory's theorem (with Bun Wong), accepted for publication in American Journal of Mathematics, arXiv:2209.08741.
• 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 and Rigidities:
• 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. MathSciNet, zbMATH, 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.
• 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
• 复环面情形的Suita猜想, Chinese Annals of Mathematics, Ser. A 35 (2014), 101--108 (in Chinese); translation: Suita Conjecture for a Complex Torus 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 (Asymptotique au bord de la métrique du noyau de Bergman relatif pour des courbes elliptiques), 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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