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Spring 2012 $L^{2}$ estimates for $\bar{\partial}$ across a divisor with Poincaré-like singularities
Dror Varolin
Illinois J. Math. 56(1): 235-249 (Spring 2012). DOI: 10.1215/ijm/1380287470

Abstract

We present results on $L^{2}$ estimates for solutions of $\bar{\partial}$-equations on a Stein manifold with a divisor. The structure of the divisor allows us to introduce weights with certain types of singularities, and the geometry of the manifold near the divisor allows us, by exploiting twisted techniques, to weaken the usual curvature hypotheses that guarantee a solution. We investigate two situations; one in which the weights are not locally integrable, and another in which they can be.

Citation

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Dror Varolin. "$L^{2}$ estimates for $\bar{\partial}$ across a divisor with Poincaré-like singularities." Illinois J. Math. 56 (1) 235 - 249, Spring 2012. https://doi.org/10.1215/ijm/1380287470

Information

Published: Spring 2012
First available in Project Euclid: 27 September 2013

zbMATH: 1280.32009
MathSciNet: MR3117028
Digital Object Identifier: 10.1215/ijm/1380287470

Subjects:
Primary: ‎32A36‎, 32F32, 32L05

Rights: Copyright © 2012 University of Illinois at Urbana-Champaign

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Vol.56 • No. 1 • Spring 2012
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