Ohsawa–Takegoshi theorem

Short description: Result concerning the holomorphic extensions In several complex variables

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