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Weighted Bergman kernels and virtual Bergman kernels [PDF]
Science in China Series A: Mathematics, 2004 We introduce the notion of "virtual Bergman kernel" and apply it to the computation of the Bergman kernel of "domains inflated by Hermitian balls", in particular when the base domain is a bounded symmetric domain.Comment: 12 pages.
A. Korányi +16 more
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Algebraicity of the Bergman kernel [PDF]
Mathematische Annalen, 2020 Our main result introduces a new way to characterize two-dimensional finite ball quotients by algebraicity of their Bergman kernels. This characterization is particular to dimension two and fails in higher dimensions, as is illustrated by a ...
P. Ebenfelt, Ming Xiao, Hangjun Xu
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Semicontinuity of the Automorphism Groups of Domains with Rough Boundary [PDF]
International Journal of Mathematics and Mathematical Sciences, 2012 Based on some ideas of Greene and Krantz, we study the semicontinuity of automorphism groups of domains in one and several complex variables. We show that semicontinuity fails for domains in , , with Lipschitz boundary, but it holds for domains in with ...
Steven G. Krantz
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Boundary asymptotics of the relative Bergman kernel metric for hyperelliptic curves
Complex Manifolds, 2017 We survey variations of the Bergman kernel and their asymptotic behaviors at degeneration. For a Legendre family of elliptic curves, the curvature form of the relative Bergman kernel metric is equal to the Poincaré metric on ℂ \ {0,1}. The cases of other
Dong Robert Xin
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Bergman kernels and symplectic reduction [PDF]
Comptes Rendus. Mathématique, 2005 We generalize several recent results concerning the asymptotic expansions of Bergman kernels to the framework of geometric quantization and establish an asymptotic symplectic identification property.
Ma, Xiaonan, Zhang, Weiping
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Bergman kernel and hyperconvexity index [PDF]
Analysis & PDE, 2016 Let $\Omega\subset {\mathbb C}^n$ be a bounded domain with the hyperconvexity index $\alpha(\Omega)>0$. Let $\varrho$ be the relative extremal function of a fixed closed ball in $\Omega$ and set $\mu:=|\varrho|(1+|\log|\varrho||)^{-1}$, $\nu:=|\varrho|(1+
Boyong Chen
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Applications of Bergman kernel functions [PDF]
, 2003 In this paper we revisit the so-called Bergman kernel method (BKM) for solving conformal mapping problems. This method is based on the reproducing property of the Bergman kernel function.
Bock, S., Falcão, M. I., Gürlebeck, K.
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The Bergman Kernel on Some Hartogs Domains [PDF]
The Journal of Geometric Analysis, 2015 We obtain new explicit formulas for the Bergman kernel function on two families of Hartogs domains. To do so, we first compute the Bergman kernels on the slices of these Hartogs domains with some coordinates fixed, evaluate these kernel functions at ...
Zhenghui Huo
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Comptes Rendus. Mathématique, 2015 It is known that the Bergman kernel associated with Lk, where L is positive line bundle over a complex compact manifold, has an asymptotic expansion. We give an elementary proof of the fact that the subprincipal term of this expansion is the scalar curvature.
L. Charles
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Bergman kernel functions associated to measures supported on totally real submanifolds [PDF]
Journal für die Reine und Angewandte Mathematik, 2022 We prove that the Bergman kernel function associated to a smooth measure supported on a piecewise-smooth maximally totally real submanifold 𝐾 in C n \mathbb{C}^{n} is of polynomial growth.
G. Marinescu, Duc-Viet Vu
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