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THE OPTIMAL JET $L^{2}$ EXTENSION OF OHSAWA–TAKEGOSHI TYPE

  • GENKI HOSONO (a1)
Abstract

We prove the $L^{2}$ extension theorem for jets with optimal estimate following the method of Berndtsson–Lempert. For this purpose, following Demailly’s construction, we consider Hermitian metrics on jet vector bundles.

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[1] Berndtsson, B., Curvature of vector bundles associated to holomorphic fibrations , Ann. of Math. (2) 169(2) (2009), 531560.
[2] Berndtsson, B. and Lempert, L., A proof of the Ohsawa–Takegoshi theorem with sharp estimates , J. Math. Soc. Japan 68(4) (2016), 14611472.
[3] Błocki, Z., Suita conjecture and the Ohsawa–Takegoshi extension theorem , Invent. Math. 193(1) (2013), 149158.
[4] Demailly, J.-P., “ Extension of holomorphic functions defined on non reduced analytic subvarieties ”, in The Legacy of Bernhard Riemann after One Hundred and Fifty Years, Vol. I, Adv. Lect. Math. (ALM) 35 , Int. Press, Somerville, MA, 2016, 191222.
[5] Grauert, H. and Remmert, R., Coherent Analytic Sheaves, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 265 , Springer, Berlin, 1984.
[6] Guan, Q. and Zhou, X., A solution of an L 2 extension problem with an optimal estimate and applications , Ann. of Math. (2) 181(3) (2015), 11391208.
[7] Kerzman, N., Hölder and L p estimates for solutions of ̄u = f in strongly pseudoconvex domains , Comm. Pure Appl. Math. 24 (1971), 301379.
[8] Ohsawa, T., On the extension of L 2 holomorphic functions. V. Effects of generalization , Nagoya Math. J. 161 (2001), 121.
[9] Ohsawa, T. and Takegoshi, K., On the extension of L 2 holomorphic functions , Math. Z. 195(2) (1987), 197204.
[10] Popovici, D., L 2 extension for jets of holomorphic sections of a Hermitian line bundle , Nagoya Math. J. 180 (2005), 134.
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Nagoya Mathematical Journal
  • ISSN: 0027-7630
  • EISSN: 2152-6842
  • URL: /core/journals/nagoya-mathematical-journal
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