Arkiv för Matematik

Weighted integral formulas on manifolds

Elin Götmark

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We present a method of finding weighted Koppelman formulas for (p, q)-forms on n-dimensional complex manifolds X which admit a vector bundle of rank n over X×X, such that the diagonal of X×X has a defining section. We apply the method to ℙn and find weighted Koppelman formulas for (p, q)-forms with values in a line bundle over ℙn. As an application, we look at the cohomology groups of (p, q)-forms over ℙn with values in various line bundles, and find explicit solutions to the $\overline{\partial}$-equation in some of the trivial groups. We also look at cohomology groups of (0, q)-forms over ℙn×ℙm with values in various line bundles. Finally, we apply our method to developing weighted Koppelman formulas on Stein manifolds.

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Ark. Mat., Volume 46, Number 1 (2008), 43-68.

Received: 13 November 2006
First available in Project Euclid: 31 January 2017

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2007 © Institut Mittag-Leffler


Götmark, Elin. Weighted integral formulas on manifolds. Ark. Mat. 46 (2008), no. 1, 43--68. doi:10.1007/s11512-007-0056-7.

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