Strict plurisubharmonicity of Bergman kernels on generalized annuli

2014 ◽  
Vol 111 (3) ◽  
pp. 237-243
Author(s):  
Yanyan Wang
Keyword(s):  
Bergman Kernels

scholarly journals BERGMAN KERNELS AND EQUILIBRIUM MEASURES FOR POLARIZED PSEUDO-CONCAVE DOMAINS

2010 ◽  
Vol 21 (01) ◽  
pp. 77-115 ◽  
Author(s):  
ROBERT J. BERMAN
Keyword(s):  
Toeplitz Operators ◽  
Equilibrium Measure ◽  
Markov Property ◽  
General Setting ◽  
Space Structure ◽  
Tensor Power ◽  
Bergman Kernels ◽  
Equilibrium Measures ◽  
Holomorphic Sections ◽  
Positive Line Bundle

Let X be a domain in a closed polarized complex manifold (Y,L), where L is a (semi-) positive line bundle over Y. Any given Hermitian metric on L induces by restriction to X a Hilbert space structure on the space of global holomorphic sections on Y with values in the k-th tensor power of L (also using a volume form ωn on X. In this paper the leading large k asymptotics for the corresponding Bergman kernels and metrics are obtained in the case when X is a pseudo-concave domain with smooth boundary (under a certain compatibility assumption). The asymptotics are expressed in terms of the curvature of L and the boundary of X. The convergence of the Bergman metrics is obtained in a more general setting where (X,ωn) is replaced by any measure satisfying a Bernstein–Markov property. As an application the (generalized) equilibrium measure of the polarized pseudo-concave domain X is computed explicitly. Applications to the zero and mass distribution of random holomorphic sections and the eigenvalue distribution of Toeplitz operators will be described elsewhere.

scholarly journals Generalized Bergman kernels on symplectic manifolds of bounded geometry

2019 ◽  
Vol 44 (11) ◽  
pp. 1037-1071 ◽  
Author(s):  
Yuri A. Kordyukov ◽  
Xiaonan Ma ◽  
George Marinescu
Keyword(s):  
Symplectic Manifolds ◽  
Bergman Kernels ◽  
Bounded Geometry
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