Kähler Spaces. Bergman Metrics. Harish-Chandra-Cartan Theorem. Siegel Space (once again!)

1997 ◽  
pp. 102-118
Author(s):  
Krzysztof Maurin
Keyword(s):  
Bergman Metrics

scholarly journals Optimal convergence speed of Bergman metrics on symplectic manifolds

2020 ◽  
Vol 18 (4) ◽  
pp. 1091-1126
Author(s):  
Wen Lu ◽  
Xiaonan Ma ◽  
George Marinescu
Keyword(s):  
Symplectic Manifolds ◽  
Convergence Speed ◽  
Optimal Convergence ◽  
Bergman Metrics

scholarly journals On the existence of Kobayashi and Bergman metrics for Model domains

2020 ◽  
Author(s):  
Nikolay Shcherbina
Keyword(s):  
Entire Function ◽  
Continuous Function ◽  
Pseudoconvex Domain ◽  
Plurisubharmonic Function ◽  
Holomorphic Curves ◽  
List Type ◽  
Bergman Metric ◽  
The Core ◽  
Bounded Smooth ◽  
Bergman Metrics

Abstract We prove that for a pseudoconvex domain of the form $${\mathfrak {A}} = \{(z, w) \in {\mathbb {C}}^2 : v > F(z, u)\}$$ A = { ( z , w ) ∈ C 2 : v > F ( z , u ) } , where $$w = u + iv$$ w = u + i v and F is a continuous function on $${\mathbb {C}}_z \times {\mathbb {R}}_u$$ C z × R u , the following conditions are equivalent: The domain $$\mathfrak {A}$$ A is Kobayashi hyperbolic. The domain $$\mathfrak {A}$$ A is Brody hyperbolic. The domain $$\mathfrak {A}$$ A possesses a Bergman metric. The domain $$\mathfrak {A}$$ A possesses a bounded smooth strictly plurisubharmonic function, i.e. the core $$\mathfrak {c}(\mathfrak {A})$$ c ( A ) of $$\mathfrak {A}$$ A is empty. The graph $$\Gamma (F)$$ Γ ( F ) of F can not be represented as a foliation by holomorphic curves of a very special form, namely, as a foliation by translations of the graph $$\Gamma ({\mathcal H})$$ Γ ( H ) of just one entire function $${\mathcal {H}} : {\mathbb {C}}_z \rightarrow {\mathbb {C}}_w$$ H : C z → C w .

scholarly journals Euclidean Embeddings and Riemannian Bergman Metrics

2015 ◽  
Vol 26 (1) ◽  
pp. 499-528
Author(s):  
Eric Potash
Keyword(s):  
Euclidean Embeddings ◽  
Bergman Metrics

On the holomorphicity of proper harmonic maps between unit balls with the Bergman metrics

2000 ◽  
Vol 316 (2) ◽  
pp. 333-354 ◽  
Author(s):  
Song-Ying Li ◽  
Lei Ni
Keyword(s):  
Harmonic Maps ◽  
Bergman Metrics

scholarly journals A REMARK ON KAZHDAN'S THEOREM ON SEQUENCES OF BERGMAN METRICS

2009 ◽  
Vol 63 (1) ◽  
pp. 133-137 ◽  
Author(s):  
Takeo OHSAWA
Keyword(s):  
Bergman Metrics

scholarly journals Stability and integration over Bergman metrics

2014 ◽  
Vol 2014 (7) ◽  
Author(s):  
Semyon Klevtsov ◽  
Steve Zelditch
Keyword(s):  
Bergman Metrics

scholarly journals Generalized Berezin quantization, Bergman metrics and fuzzy laplacians

2008 ◽  
Vol 2008 (09) ◽  
pp. 059-059 ◽  
Author(s):  
Calin Iuliu Lazaroiu ◽  
Daniel McNamee ◽  
Christian Sämann
Keyword(s):  
Berezin Quantization ◽  
Bergman Metrics
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