In
several complex variables, the Ohsawa–Takegoshi ''L''
2 extension theorem is a fundamental result concerning the
holomorphic
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood of each point in a domain in complex coordinate space . The existence of a complex derivati ...
extension of an
-holomorphic function defined on a bounded
Stein manifold In mathematics, in the theory of several complex variables and complex manifolds, a Stein manifold is a complex submanifold of the vector space of ''n'' complex dimensions. They were introduced by and named after . A Stein space is similar to a Ste ...
(such as a
pseudoconvex compact
Compact as used in politics may refer broadly to a pact or treaty; in more specific cases it may refer to:
* Interstate compact
* Blood compact, an ancient ritual of the Philippines
* Compact government, a type of colonial rule utilized in British ...
set in
of dimension less than
) 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.
See also
*
Suita conjecture
note
References
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External links
*
Analytic Methods in Algebraic Geometry
{{DEFAULTSORT:Ohsawa-Takegoshi L2 extension theorem
Mathematical theorems
Several complex variables