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Conditions for the \( \bar \partial \)-closedness of differential forms

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Abstract

The \( \bar \partial \)-closed differential forms with smooth coefficients are studied in the closure of a bounded domain D ⊂ ℂn. It is demonstrated that the condition of \( \bar \partial \)-closedness can be replaced with a weaker differential condition in the domain and differential conditions on the boundary. In particular, for the forms with harmonic coefficients the \( \bar \partial \)-closedness is equivalent to some boundary relations. This allows us to treat the results as conditions for the \( \bar \partial \)-closedness of an extension of a form from the boundary.

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Authors and Affiliations

  1. Siberian Federal University, Krasnoyarsk, Russia

    A. M. Kytmanov & S. G. Myslivets

Authors
  1. A. M. Kytmanov
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  2. S. G. Myslivets
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Correspondence to A. M. Kytmanov.

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Original Russian Text Copyright © 2009 Kytmanov A. M. and Myslivets S. G.

The authors were supported by the Russian Foundation for Basic Research (Grants 08-01-00844 and 08-01-90250).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 6, pp. 1333–1347, November–December, 2009.

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Kytmanov, A.M., Myslivets, S.G. Conditions for the \( \bar \partial \)-closedness of differential forms. Sib Math J 50, 1049–1061 (2009). https://doi.org/10.1007/s11202-009-0116-2

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  • DOI: https://doi.org/10.1007/s11202-009-0116-2

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