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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