On the extension of L² holomorphic functions V-Effects of generalization

Abstract

Abstract. A general extension theorem for L 2 holomorphic bundle-valued top forms is formulated. Although its proof is based on a principle similar to Ohsawa-Takegoshi's extension theorem, it explains previous L 2 extendability results systematically and bridges extension theory and division theory.

Strong openness of multiplier ideal sheaves and optimal L 2 extension

“…The optimal L 2 extension and applications. Now let's recall some notations in [41]. Let M be a complex n−dimensional manifold, and S be a closed complex subvariety of M .…”

Restricted Bergman kernel asymptotics

“…But it seems to be unknown. Theorem 1.4 can be derived from Theorem 4 of [Ohs01] by a standard approximation technique. See also [Kim10].…”

Weighted Bergman kernel: asymptotic behavior, applications and comparison results

“…for all z ∈ D ∩ V (the proof is the same as in Ohsawa [24], although he only considered the classical Bergman kernel function).…”

“…An extension theorem of Ohsawa and applications. Recently, Ohsawa [24] obtained a general L 2 -extension theorem from which one can deduce all the earlier extension theorems. However, to state this theorem completely is quite laborious.…”

“…[24]). Hence the above corollary applies in particular to any bounded pseudoconvex domain with Lipschitz boundary.…”