The bergman metric and the pluricomplex green function
By Zbigniew Blocki. 2005
79 citations recorded by the source corpus.
We improve a lower bound for the Bergman distance in smooth pseudoconvex domains due to Diederich and Ohsawa. As the main tool we use the pluricomplex Green function and an L 2 -estimate for the ∂-operator of Donnelly and Fefferman.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/9e4129e4d44862532722d31e0cb5704a4d69f97c
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Suita conjecture and the Ohsawa-Takegoshi extension theorem (2013, unknown): “It was observed in [4] that (2) makes also sense (and indeed remains true) for arbitrary plurisubharmonic φ: instead of |α|2 i∂∂̄φ one should take any H ∈ L∞loc(Ω) with iᾱ ∧ α ≤ H i∂∂̄φ.”
- Comparison of the Bergman and Szegö kernels (2010, methodology): “the L2-estimates for the ∂¯-operator by H¨ormander [26], Demailly [14], and Berndtsson [2]. We also make essential use of Blocki’s estimates for the pluricomplex Green function on hyperconvex domains [4]. This paper is organized as follows: In Section 2, we establish necessary background for the Har”