Rawnsley’s <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" id="d1e19" altimg="si12.gif"><mml:mi>ε</mml:mi></mml:math>-function on some Hartogs type domains over bounded symmetric domains and its applications

Bi, Enchao; Feng, Zhiming; Su, Guicong; Tu, Zhenhan

doi:10.1016/j.geomphys.2018.10.003

Cited by 7 publications

(1 citation statement)

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“…As far as we know, the above conditions are satisfied by homogeneous Kähler manifold, a contractible homogeneous Kähler manifold (i.e., all the products ( , g) × (ℂ m , g 0 ) , where ( , g) is an homogeneous bounded domain and g 0 is the standard flat metric) and some special pseudoconvex domains (cf. [4,19,26,30]). So some experts are dedicated to find more noncompact Kähler manifolds which a Berezin quantization can be carried out.…”

Section: Remark 13 Notice That Ifmentioning

confidence: 99%

Balanced metrics and Berezin quantization on Hartogs triangles

2020

Annali di Matematica

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In this paper, we study balanced metrics and Berezin quantization on a class of Hartogs domains defined by $$\varOmega _n=\{(z_1,\ldots ,z_n)\in {\mathbb {C}}^n:\vert z_1\vert<\vert z_2\vert<\cdots<\vert z_n\vert <1\}$$ Ω n = { ( z 1 , … , z n ) ∈ C n : | z 1 | < | z 2 | < ⋯ < | z n | < 1 } which generalize the so-called classical Hartogs triangle. We introduce a Kähler metric $$g(\nu )$$ g ( ν ) associated with the Kähler potential $$\varPhi _n(z):=-\sum _{k=1}^{n-1}\nu _k\ln (\vert z_{k+1}\vert ^2-\vert z_k\vert ^2)-\nu _n\ln (1-\vert z_n\vert ^2)$$ Φ n ( z ) : = - ∑ k = 1 n - 1 ν k ln ( | z k + 1 | 2 - | z k | 2 ) - ν n ln ( 1 - | z n | 2 ) on $$\varOmega _n$$ Ω n . As main contributions, on one hand we compute the explicit form for Bergman kernel of weighted Hilbert space, and then, we obtain the necessary and sufficient condition for the metric $$g(\nu )$$ g ( ν ) on the domain $$\varOmega _n$$ Ω n to be a balanced metric. On the other hand, by using the Calabi’s diastasis function, we prove that the Hartogs triangles admit a Berezin quantization.

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Section: Remark 13 Notice That Ifmentioning

confidence: 99%