L-2 extension for jets of holomorphic sections of a Hermitian line bundle
UNSPECIFIED (2005) L-2 extension for jets of holomorphic sections of a Hermitian line bundle. NAGOYA MATHEMATICAL JOURNAL, 180 . pp. 1-34. ISSN 0027-7630Full text not available from this repository.
Let (X, omega) be a weakly pseudoconvex Kahler manifold, Y subset of X a closed submanifold defined by some holomorphic section of a vector bundle over X, and L a Hermitian line bundle satisfying certain positivity conditions. We prove that for any integer k >= 0, any section of the jet sheaf L circle times O (x)/I-Y(k+1) which satisfies a certain L-2 condition, can be extended into a global holomorphic section of L over X whose L-2 growth on an arbitrary compact subset of X is under control. In particular, if Y is merely a point, this gives the existence of a global holomorphic function with an L-2 norm under control and with prescribed values for all its derivatives up to order k at that point. This result generalizes the L-2 extension theorems of Ohsawa-Takegoshi and of Manivel to the case of jets of sections of a line bundle. A technical difficulty is to achieve uniformity in the constant appearing in the final estimate. To this end, we make use of the exponential map and of a Rauch-type comparison theorem for complete Riemannian manifolds.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Journal or Publication Title:||NAGOYA MATHEMATICAL JOURNAL|
|Number of Pages:||34|
|Page Range:||pp. 1-34|
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