A proof of the Ohsawa–Takegoshi theorem with sharp estimates

By B. Berndtsson, László Lempert. 2014

101 citations recorded by the source corpus.

We give a proof of the Ohsawa-Takegoshi extension theorem with sharp estimates. The proof is based on ideas of Blocki to use variations of domains to simplify his proof of the Suita conjecture, and also uses positivity properties of direct image bundles.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/cf3a1126bed3d06f7e65a1409b46d8c62da60978

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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, background): “rucial contribution of [OT87, Ohs88], this resulthas been generalizedbymanyauthorsin variouscontexts, including [Man93], [Dem00], [Siu04], [Ber05], [Che11], [Yi12], [ZGZ12], [Blo13], [GZ15a],[Dem15], [BL16]. In this article we treat yet another version of the extension theorem in the context of Kahl”
Extension of holomorphic functions defined on non reduced analytic subvarieties (2015, background): “qualities, section 4 elaborates on the concept of jumping numbers for multiplier ideal sheaves, and section 5 explains the technical details of the L2 estimates and their proofs. We refer to [Ber96], [BL14], [Blo13], [Che11], [DHP13], [GZ13,15], [Man93], [MV07], [Ohs88,94,95,01,03,05], [Pop05], [Var”
Algebraic fiber spaces over abelian varieties: around a recent theorem by Cao and Paun (2016, methodology): “on the Ohsawa-Takegoshi extension theorem with sharp estimates, recently proved by Blo cki and Guan-Zhou [Blo 13, GZ15]. This approach was suggested to us by Mihai Pa˘un. Note. Berndtsson and Lempert [BL16] explain how one can use the curvature properties of pushforwards of adjoint bundles to get a ”
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.”