# [2] Berndtsson B. Curvature of vector bundles and subharmonicity of the [5] Lempert L. Solving the degenerate complex Monge-Ampère

that, a new proof of the optimal estimate was given by Berndtsson{Lempert. Using their method, we will give a jet version of the L2 extension theorem with an optimal estimate. We also give a sharper estimate 3. of the L2 extension theorem using Hartogs domains. Dinh Tuan Huynh (Osaka University)

Publiceringsår: 2016. Publicerat i: Journal of the Mathematical Society of Japan. Publikationstyp: Artikel i 2016. A proof of the Ohsawa-Takegoshi theorem with sharp estimates. Bo Berndtsson, L. Lempert. Journal of the Mathematical Society of Japan.

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Journal of the Mathematical Society of Japan 68 (4), 1461-1472, 2016. 61: 2016: Strict and nonstrict positivity of direct image bundles. B Berndtsson. Mathematische Zeitschrift 269 (3-4), 1201-1218, 2011. 54: 2011: Bergman kernels related to Hermitian line bundles over compact complex manifolds. We follow the variational proof by Berndtsson-Lempert and use the method in the paper of McNeal-Varolin. As an application, we give an optimal estimate for extensions from possibly non-reduced subvarieties.

Since Suita conjecture was proved by B locki[3] based on a sharp version of the Ohsawa-Takegoshi theorem, some other approaches to prove this conjecture appeared, for example in [4] . A much simpler way proposed by Lempert is to use the plurisubharmonic variation of the Bergman kernels. Lempert, László Abstract We show how ideas from \cite{2Blocki} and \cite{3Blocki} to prove the Suita conjecture can be adapted to give a proof of the Ohsawa-Takegoshi extension theorem with sharp estimates.

## Apr 10, 2013 - A Bicycle Coloring Book features a four color cover and 26 gorgeous line drawings by artist Taliah Lempert. Sparad av Mathias Berntsson.

Leo - 664. Levan - 665. Lewenhaupt - 666 S: Larsson, Stig Peter G K: Berndtsson, Carl Henrik 1941.

### A. Guan and X.-Y. Zhou. In Chapter 4, various results on the Bergman kernel are presented, including recent works of Maitani–Yamaguchi, Berndtsson, Guan–Zhou, and Berndtsson–Lempert. Most of these results are obtained by the L² method. In the last chapter, rather specific results are discussed on the existence and classification of

We also give a sharper estimate 3. of the L2 extension theorem using Hartogs domains. Dinh Tuan Huynh (Osaka University) Bo Berndtsson, Dario Cordero-Erausquin, Bo’Az Klartag et al Journal of the European Mathematical Society. Vol. 22 (2), p. 477-505 Amazon.in - Buy L² Approaches in Several Complex Variables: Towards the Oka–Cartan Theory with Precise Bounds (Springer Monographs in Mathematics) book online at best prices in India on Amazon.in. Read L² Approaches in Several Complex Variables: Towards the Oka–Cartan Theory with Precise Bounds (Springer Monographs in Mathematics) book reviews & author details and more at Amazon.in. Free [ Abstract ] We present a new method in constructing 5-dimensional stationary solutions to the vacuum Einstein equation.

We give a proof of the Ohsawa–Takegoshi extension theorem with sharp estimates. The proof is based on ideas of Bˆlocki to use variations of domains to simplify his proof of the Suita conjecture, and also uses positivity properties of direct
Roughly speaking, by the works of Guan-Zhou and Berndtsson-Lempert, the Ohsawa-Takegoshi type extension theorems with optimal estimate and the positivity of the twisted relative canonical bundle
the method of Berndtsson-Lempert. For this purpose, following Demailly’s construction, we consider Hermitian metrics on jet vector bundles. 1. Introduction The Ohsawa-Takegoshi L2 extension theorem, ﬁrst proved in [OT], is one of the most important theorems in complex geometry and several complex variables.

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Anna Berntsson - Pommac 6.

L² Approaches in Several Complex Variables: Towards the Oka-Cartan Theory with Precise Bounds: Ohsawa, Takeo: Amazon.nl
2017-07-01
2018-02-16
Author: Bo Berndtsson; L. Lempert Published: 2016 Published in: Journal of the Mathematical Society of Japan
We give a proof of the Ohsawa–Takegoshi extension theorem with sharp estimates.

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### Kähler-Einstein metrics singular along a smooth divisor · Laszlo Lempert, La powers of complex line bundles, based on joint works with B. Berndtsson and

A much simpler way proposed by Lempert is to use the plurisubharmonic variation of the Bergman kernels. This monograph presents the current status of a rapidly developing part of several complex variables, motivated by the applicability of effective results to algebraic geometry and differential geometry. Special emphasis is put on the new precise results on the L(2) extension of holomorphic functions in the past 5 years.In Chapter 1, the classical questions of several complex variables Their proof is also based on Berndtsson-Lempert, but there are some differences. 2017/11/24 Colloquium.