On extending $L^{2}$ holomorphic functions from complex hyperplanes

Details On extending $L^{2}$ holomorphic functions from complex hyperplanes On extending $L^{2}$ holomorphic functions from complex hyperplanes

2011-04-21

arxiv.org/abs/1104.4305v2

Mathematics

Complex Variables

This paper has been withdrawn by the authors due to an error in estimate (5). Correcting the estimate leads to a fractional ex

Scientific paper

The key to the proof of the Ohsawa-Takegoshi Extension Theorem is a certain $\bar{\partial}$-estimate. The purpose of this note is to show that the 'curvature term' that arises in the Kohn-Morrey-H\"{o}rmander inequality (or the Bochner-Kodaira technique) is sufficient to produce such an estimate. We exploit self boundedness of the gradients of the weight functions to change the weight with respect to which the adjoint is taken. The weights, on the other hand, are the usual ones used in this context.

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