Suita conjecture and the Ohsawa-Takegoshi extension theorem

By Zbigniew Blocki. 2013

202 citations recorded by the source corpus.

We prove a conjecture of N. Suita which says that for any bounded domain D in ℂ one has $c_{D}^{2}\leq\pi K_{D}$, where cD(z) is the logarithmic capacity of ℂ∖D with respect to z∈D and KD the Bergman kernel on the diagonal. We also obtain optimal constant in the Ohsawa-Takegoshi extension theorem.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7bfea03358853d41c510e1486d4075ca348b3579

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Ohsawa-Takegoshi Extension Theorem for Compact Kähler Manifolds and Applications (2014, methodology): “are using in an essential manner the existence of Zariski dense open subsets of X. We will state next our general version of Theorem 1.1; prior to this, we introduce some auxiliary weights, following [Blo13], [GZ15a]. Notations 1. Given δ > 0 and A ∈ R, let cA(t) be a positive smooth function on ”
Positivity of twisted relative pluricanonical bundles and their direct images (2014, methodology): “It relies on the version of the Ohsawa-Takegoshi extension theorem obtained by B locki [6] and Guan-Zhou [21], combined with an approach due to Tsuji.”
A solution of an $L^{2}$ extension problem with optimal estimate and applications (2013, result): “log|w(z)|) on Ω (see [47]). Suita’s conjecture in [53] says that on any open Riemann surface Ω as above, (cβ(z0))2 ≤ πBΩ(z0). The above conjecture was ﬁrst proved for bounded planar domains by Blocki [11, 12], and then by Guan-Zhou [29] for open Riemann surfaces. For earlier works, see [61]. In the ”
Kodaira dimension of algebraic fiber spaces over abelian varieties (2015, unknown): “([5]), ([1]) Let p : X → D be a projective family over the unit ball in C, and let (L, hL) → X be a Hermitian line bundle.”