Boundary behavior of the Bergman metric
نویسندگان
چکیده
منابع مشابه
On the boundary behavior of the holomorphic sectional curvature of the Bergman metric
We obtain a conceptually new differential geometric proof of P.F. Klembeck’s result (cf. [9]) that the holomorphic sectional curvature kg(z) of the Bergman metric of a strictly pseudoconvex domain Ω ⊂ C approaches −4/(n + 1) (the constant sectional curvature of the Bergman metric of the unit ball) as z → ∂Ω.
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It is proved that on any bounded domain in the complex Euclidean space C(n) the Bergman metric is always greater than or equal to the Carathéodory distance. This leads to a number of interesting consequences. Here two such consequences are given. (i) The Bergman metric is complete whenever the Carathéodory distance is complete on a bounded domain. (ii) The Weil-Petersson metric is not uniformly...
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If D is a bounded open subset of C", the set H = {ƒ: D —> C| ƒ is holomorphic and SD\f\ 2 < +°°} is a separable infinite-dimensional Hubert space relative to the inner product <ƒ, g) = fDfg. The completeness of H can be seen from Cauchy integral estimates. Similar estimates show that for any p E D the functional ƒ H* ƒ(/?),ƒ£ H, is continuous. Thus there is a unique element KD(z, p) E f/ (as a ...
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In the paper Gaussian curvature of Bergman metric on the unit disc and the dependence of this curvature on the weight function has been studied.
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We present a method of obtaining a lower bound estimate of the curvatures of the Bergman metric without using the regularity of the kernel function on the boundary. As an application, we prove the existence of an uniform lower bound of the bisectional curvatures of the Bergman metric of a smooth bounded pseudoconvex domain near the boundary with constant Levi rank.
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ژورنال
عنوان ژورنال: Asian Journal of Mathematics
سال: 2018
ISSN: 1093-6106,1945-0036
DOI: 10.4310/ajm.2018.v22.n2.a6