Ohsawa–Takegoshi L² extension theorem

In several complex variables, the Ohsawa–Takegoshi L² extension theorem is a fundamental result concerning the holomorphic extension of an ${\displaystyle L^{2}}$-holomorphic function defined on a bounded Stein manifold (such as a pseudoconvex compact set in ${\displaystyle \mathbb {C} ^{n}}$ of dimension less than ${\displaystyle n}$) to a domain of higher dimension, with a bound on the growth. It was discovered by Takeo Ohsawa and Kensho Takegoshi in 1987,[1] using what have been described as ad hoc methods involving twisted Laplace–Beltrami operators, but simpler proofs have since been discovered.[2] Many generalizations and similar results exist, and are known as theorems of Ohsawa–Takegoshi type.