On the Ohsawa-Takegoshi-Manivel L 2 extension theorem

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Intrinsic capacities on compact Kähler manifolds (2004, background): “2) 2 j 2 j There is also a reverse inequality which uses a deep extension result of Ohsawa-TakegoshiManivel (see [14]): There exists j0 ~ N and C4 > 0 large enough so that Yx ~ X, u ~ N, there exists s ~ F(X, L j) with fx lslae-Xhj,jo < .”
A subadditivity property of multiplier ideals. (2000, methodology): “Using the same notation as in [7], we take a plurisubharmonic function φ and denote by J (φ) the sheaf of germs of holomorphic functions f on X such that ∫ |f |(2)edV converges on a neighborhood of the given point.”
A solution of an $L^{2}$ extension problem with optimal estimate and applications (2013, background): “([36] and [17]) Let (X, g) be a Stein n-dimensional manifold possessing a Kähler metric g, and let L (resp.”
A proof of Demailly's strong openness conjecture (2015, methodology): “1 by the method of induction, and confirm every step of induction by contradiction and by using movably the Ohsawa-Takegoshi L2 extension theorem ([26]; see also [28], [1], [6], [29], etc.”