143 citations · 171 across the 13 of their papers we have counts for
14 papers
Local Rigidity of the Bergman Metric and of the Kähler Carathéodory Metric
Robert Xin Dong, Ruoyi Wang, Bun Wong
We prove that if the Carathéodory metric on a strictly pseudoconvex domain with a smooth boundary is locally Kähler near the boundary, then the domain is biholomorphic to a ball. W…
Bergman representative coordinate, constant holomorphic curvature and a multidimensional generalization of Carathéodory's theorem
Robert Xin Dong, Bun Wong
By using the Bergman representative coordinate and Calabi's diastasis, we extend a theorem of Lu to bounded pseudoconvex domains whose Bergman metric is incomplete with constant ho…
Rigidity theorems by capacities and kernels
Robert Xin Dong, John N. Treuer, Yuan Zhang
For any open hyperbolic Riemann surface , the Bergman kernel , the logarithmic capacity , and the analytic capacity satisfy the inequality chain $πK \geq c^2_β \…
Bergman-Calabi diastasis and Kähler metric of constant holomorphic sectional curvature
Robert Xin Dong, Bun Wong
We prove that for a bounded domain in with the Bergman metric of constant holomorphic sectional curvature being biholomorphic to a ball is equivalent to the hyperconv…
Rigidity theorems by the logarithmic capacity
Robert Xin Dong, Yuan Zhang
In light of the Suita conjecture, we explore various rigidity phenomena concerning the Bergman kernel, logarithmic capacity, Green's function, and Euclidean distance and volume.
Uniform estimates for the canonical solution to the -equation on product domains
Robert Xin Dong, Yifei Pan, Yuan Zhang
We obtain uniform estimates for the canonical solution to on the Cartesian product of bounded planar domains with boundaries, when is continuous up to…
Boundary asymptotics of the relative Bergman kernel metric for curves
Robert Xin Dong
We study the behaviors of the relative Bergman kernel metrics on holomorphic families of degenerating hyperelliptic Riemann surfaces and their Jacobian varieties. Near a node or cu…
Rigidity theorem by the minimal point of the Bergman kernel
Robert Xin Dong, John Treuer
We use the Suita conjecture (now a theorem) to prove that for any domain its Bergman kernel satisfies …
Sharp pointwise and uniform estimates for
Robert Xin Dong, Song-Ying Li, John N. Treuer
We use weighted -methods to obtain sharp pointwise estimates for the canonical solution to the equation on smoothly bounded strictly convex domains and the…
Equality in Suita's conjecture and metrics of constant Gaussian curvature
Robert Xin Dong
Without using the extension theorem, we provide a new proof of the equality part in Suita's conjecture, which states that for any open Riemann surface admitting a Green's fun…
Evans-Selberg potential on planar domains
Robert Xin Dong
We provide explicit formulas of Evans kernels, Evans-Selberg potentials and fundamental metrics on potential-theoretically parabolic planar domains.
Suita conjecture for a punctured torus
Robert Xin Dong
For a once-punctured complex torus, we compare the Bergman kernel and the fundamental metric, by constructing explicitly the Evans-Selberg potential and discussing its asymptotic b…
Suita Conjecture for a Complex Torus
Robert Xin Dong
The author proves that the generalized Suita conjecture holds for any complex torus, which means that , being the modified logarithmic capacity an…
Exact diagonalization: the Bose-Hubbard model as an example
J. M. Zhang, R. X. Dong
We take the Bose-Hubbard model to illustrate exact diagonalization techniques in a pedagogical way. We follow the road of first generating all the basis vectors, then setting up th…