UNSPECIFIED (2005) L-2 extension for jets of holomorphic sections of a Hermitian line bundle. NAGOYA MATHEMATICAL JOURNAL, 180 . pp. 1-34. ISSN 0027-7630

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Abstract

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
Publisher:	NAGOYA UNIV
ISSN:	0027-7630
Date:	December 2005
Volume:	180
Number of Pages:	34
Page Range:	pp. 1-34
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/34075

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