ref.bib

@book{Demailly2000,
author="Demailly, Jean-Pierre",
editor="Dolbeault, P.
and Iordan, A.
and Henkin, G.
and Skoda, H.
and Tr{\'e}preau, J.-M.",
title="On the Ohsawa-Takegoshi-Manivel $L^2$ extension theorem",
booktitle="Complex Analysis and Geometry",
year="2000",
publisher="Birkh{\"a}user Basel",
pages="47--82",
abstract="One of the goals of this work is to demonstrate in several different ways the strength of the fundamental tools introduced by Pierre Lelong for the study of Complex Analysis and Analytic or Algebraic Geometry. We first give a detailed presentation of the Ohsawa-Takegoshi L2 extension theorem, inspired by a geometric viewpoint introduced by L. Manivel in 1993. Meanwhile, we simplify the original approach of the above authors, and point out a difficulty (yet to be overcome) in the regularity argument invoked by Manivel in bidegree (0, q), q ≥ 1. We then derive some striking consequences of the L2 extension theorem. In particular, we give an approximation theorem of plurisubharmonic functions by logarithms of holomorphic functions, preserving as much as possible the singularities and Lelong numbers of the given function. The study of plurisubharmonic singularities is pursued, leading to a new Brian{\c{c}}on-Skoda type result concerning Nadel `s multiplier ideal sheaves. Using this result and some ideas of R Lazarsfeld, we finally give a new proof of a recent result of T. Fujita: the growth of the number of sections of multiples of a big line bundle is given by the highest power of the first Chern class of the numerically effective part in the line bundle Zariski decomposition.",
}


@article{Guan2015ASO,
  title={A solution of an $L^2$ extension problem with an optimal estimate and applications},
  author={Qi'an Guan and Xiangyu Zhou},
  journal={Annals of Mathematics},
  year={2015},
  volume={181},
  pages={1139-1208},
  url={https://api.semanticscholar.org/CorpusID:264249609}
}

@article{Popovici2004L2EF,
  title={L2 Extension for jets of holomorphic sections of a Hermitian line Bundle},
  author={Dan Popovici},
  journal={Nagoya Mathematical Journal},
  year={2004},
  volume={180},
  pages={1 - 34},
}

@article{ZZ18,
author = {Xiangyu Zhou and Langfeng Zhu},
title = {{An optimal $L^2$ extension theorem on weakly pseudoconvex Kähler manifolds}},
volume = {110},
journal = {Journal of Differential Geometry},
number = {1},
publisher = {Lehigh University},
pages = {135 -- 186},
keywords = {Kähler manifold, optimal $L^2$ extension, plurisubharmonic function, singular Hermitian metric, weakly pseudoconvex manifold},
year = {2018},
doi = {10.4310/jdg/1536285628},
URL = {https://doi.org/10.4310/jdg/1536285628}
}


@article{OhsawaTakegoshi1987,
  author    = {T. Ohsawa and K. Takegoshi},
  title     = {On the extension of $L^2$ holomorphic functions},
  journal   = {Mathematische Zeitschrift},
  volume    = {195},
  pages     = {197--204},
  year      = {1987},
  doi       = {10.1007/BF01166457},
}

@article{Manivel1993,
  author = {L. Manivel},
  title = {Un théorème de prolongement $L^2$ de sections holomorphes d'un fibré hermitien},
  journal = {Mathematische Zeitschrift},
  volume = {212},
  pages = {107--122},
  year = {1993},
  doi = {10.1007/BF02571643},
  url = {https://doi.org/10.1007/BF02571643}
}

@article{MV06,
author = {McNeal, Jeffery and Varolin, Dror},
year = {2006},
month = {08},
pages = {},
title = {Analytic Inversion of Adjunction. $L^2$ extension theorems with gain},
volume = {57},
journal = {Annales de l’institut Fourier},
doi = {10.5802/aif.2273}
}

@article{BZ13,
author = {Błocki, Zbigniew},
year = {2013},
month = {07},
pages = {},
title = {Suita conjecture and the Ohsawa-Takegoshi extension theorem},
volume = {193},
journal = {Inventiones mathematicae},
doi = {10.1007/s00222-012-0423-2}
}


@book{Demailly2015,
author="Demailly, Jean-Pierre",
editor="Byun, Jisoo
and Cho, Hong Rae
and Kim, Sung Yeon
and Lee, Kang-Hyurk
and Park, Jong-Do",
title="Extension of Holomorphic Functions and Cohomology Classes from Non Reduced Analytic Subvarieties",
booktitle="Geometric Complex Analysis",
year="2018",
publisher="Springer Singapore",
pages="97--113",
abstract="The goal of this survey is to describe some recent results concerning the {\$}{\$}L^{\{}2{\}}{\$}{\$}L2extension of holomorphic sections or cohomology classes with values in vector bundles satisfying weak semi-positivity properties. The results presented here are generalized versions of the Ohsawa--Takegoshi extension theorem, and borrow many techniques from the long series of papers by T. Ohsawa. The recent achievement that we want to point out is that the surjectivity property holds true for restriction morphisms to non necessarily reduced subvarieties, provided these are defined as zero varieties of multiplier ideal sheaves. The new idea involved to approach the existence problem is to make use of {\$}{\$}L^{\{}2{\}}{\$}{\$}L2approximation in the Bochner-Kodaira technique. The extension results hold under curvature conditions that look pretty optimal. However, a major unsolved problem is to obtain natural (and hopefully best possible) {\$}{\$}L^{\{}2{\}}{\$}{\$}L2estimates for the extension in the case of non reduced subvarieties---the case when Y has singularities or several irreducible components is also a substantial issue.",
isbn="978-981-13-1672-2"
}
@article{HG17,
author = {Hosono, Genki},
year = {2017},
month = {06},
pages = {},
title = {The optimal jet $L^2$ extension of Ohsawa-Takegoshi type},
volume = {239},
journal = {Nagoya Mathematical Journal},
doi = {10.1017/nmj.2018.31}
}

@article{BB14,
author = {Berndtsson, Bo and Lempert, László},
year = {2014},
month = {07},
pages = {},
title = {A proof of the Ohsawa-Takegoshi theorem with sharp estimates},
volume = {68},
journal = {Journal of the Mathematical Society of Japan},
doi = {10.2969/jmsj/06841461}
}

@article{MJV17,
       author = {{McNeal}, Jeffery D. and {Varolin}, Dror},
        title = "{Extension of Jets With $L^2$ Estimates, and an Application}",
      journal = {arXiv e-prints},
     keywords = {Mathematics - Complex Variables},
         year = 2017,
        month = jul,
          eid = {arXiv:1707.04483},
        pages = {arXiv:1707.04483},
          doi = {10.48550/arXiv.1707.04483},
archivePrefix = {arXiv},
       eprint = {1707.04483},
 primaryClass = {math.CV},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2017arXiv170704483M},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}


@article{GZ12,
author = {Zhu, Langfeng and Guan, Qian and Zhou, Xiangyu},
year = {2012},
month = {06},
pages = {},
title = {On the Ohsawa-Takegoshi $L^2$ extension theorem and the Bochner-Kodaira identity with non-smooth twist factor},
volume = {97},
journal = {Journal De Mathematiques Pures Et Appliquees - J MATH PURE APPL},
doi = {10.1016/j.matpur.2011.09.010}
}


@article{GZ13,
author = {Guan, Qian and Zhou, Xiangyu},
year = {2013},
month = {10},
pages = {},
title = {A solution of $L^{2}$ extension problem with optimal estimate and applications},
volume = {181},
journal = {Annals of Mathematics},
doi = {10.4007/annals.2015.181.3.6}
}

@article{GZ18,
author = {Zhou, Xiangyu and Zhu, Langfeng},
year = {2018},
month = {12},
pages = {},
title = {Siu's lemma, optimal $L^2$ extension and applications to twisted pluricanonical sheaves},
volume = {377},
journal = {Mathematische Annalen},
doi = {10.1007/s00208-018-1783-8}
}

@article{CR22,
author = {Chen, Jian and Rao, Sheng},
year = {2022},
month = {05},
pages = {},
title = {$L^2$ Extension of $\bar\partial$-Closed Forms on Weakly Pseudoconvex Kähler Manifolds},
volume = {32},
journal = {The Journal of Geometric Analysis},
doi = {10.1007/s12220-022-00886-3}
}


@article{Demailly1982,
  author = {Jean-Pierre Demailly},
  title = {Estimations $L^2$ pour l'opérateur $\bar\partial$ d’un fibré vectoriel holomorphe semi-positif au-dessus d’une variété kählérienne complète},
  journal = {Annales scientifiques de l'École Normale Supé-rieure, Serie 4},
  volume = {15},
  number = {3},
  year = {1982},
  pages = {457-511},
  doi = {10.24033/asens.1434},
  url = {http://www.numdam.org/articles/10.24033/asens.1434/}
}

@book{Hormander1990,
  author = {Lars H\"ormander},
  title = {An Introduction to Complex Analysis in Several Variables},
  edition = {3},
  series = {North-Hol\\ land Mathematical Library},
  number = {7},
  publisher = {North-Holland Publishing Co.},
  address = {Amsterdam},
  year = {1990},
  mrnumber = {1045639},
  zblnumber = {0685.32001}
}