Formulas that relate the Bergman kernel and projection of a bounded Reinhardt domain whose closur... more Formulas that relate the Bergman kernel and projection of a bounded Reinhardt domain whose closure does not intersect the coordinate planes to those of its covering tube domain are obtained via the Poisson summation formula.
The Bergman kernel is encoded with information on algebraic and geometric structures of the under... more The Bergman kernel is encoded with information on algebraic and geometric structures of the underlying complex manifolds. How the Bergman kernel behaves as the underlying structures deform is a problem that has been extensively studied in a number of settings. This talk is about stability of the Bergman kernel on a tower of coverings of complex manifolds Mj = f M= j, where f jg are free and properly discontinuous groups of automorphisms of f
Proceedings of the American Mathematical Society, 1999
We show how to compute the Bergman kernel functions of some special domains in a simple way. As a... more We show how to compute the Bergman kernel functions of some special domains in a simple way. As an application of the explicit formulas, we show that the Bergman kernel functions of some convex domains, for instance the domain in C 3 \mathbb {C}^3 defined by the inequality | z 1 | + | z 2 | + | z 3 | > 1 |z_1|+|z_2|+|z_3|>1 , have zeroes.
Proceedings of the American Mathematical Society, 1994
In this note we obtain a sharp estimate of the Bergman kernels near C 2 {\mathcal {C}^2} boundary... more In this note we obtain a sharp estimate of the Bergman kernels near C 2 {\mathcal {C}^2} boundary points of pseudoconvex domains by induction on the dimension and a theorem of Ohsawa-Takegoshi.
Formulas that relate the Bergman kernel and projection of a bounded Reinhardt domain whose closur... more Formulas that relate the Bergman kernel and projection of a bounded Reinhardt domain whose closure does not intersect the coordinate planes to those of its covering tube domain are obtained via the Poisson summation formula.
The Bergman kernel is encoded with information on algebraic and geometric structures of the under... more The Bergman kernel is encoded with information on algebraic and geometric structures of the underlying complex manifolds. How the Bergman kernel behaves as the underlying structures deform is a problem that has been extensively studied in a number of settings. This talk is about stability of the Bergman kernel on a tower of coverings of complex manifolds Mj = f M= j, where f jg are free and properly discontinuous groups of automorphisms of f
Proceedings of the American Mathematical Society, 1999
We show how to compute the Bergman kernel functions of some special domains in a simple way. As a... more We show how to compute the Bergman kernel functions of some special domains in a simple way. As an application of the explicit formulas, we show that the Bergman kernel functions of some convex domains, for instance the domain in C 3 \mathbb {C}^3 defined by the inequality | z 1 | + | z 2 | + | z 3 | > 1 |z_1|+|z_2|+|z_3|>1 , have zeroes.
Proceedings of the American Mathematical Society, 1994
In this note we obtain a sharp estimate of the Bergman kernels near C 2 {\mathcal {C}^2} boundary... more In this note we obtain a sharp estimate of the Bergman kernels near C 2 {\mathcal {C}^2} boundary points of pseudoconvex domains by induction on the dimension and a theorem of Ohsawa-Takegoshi.
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