Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Kohn decomposition for forms on coverings of complex manifolds constrained along fibres
HTML articles powered by AMS MathViewer

by A. Brudnyi and D. Kinzebulatov PDF
Trans. Amer. Math. Soc. 369 (2017), 167-186 Request permission


The classical result of J.J. Kohn asserts that over a relatively compact subdomain $D$ with $C^\infty$ boundary of a Hermitian manifold whose Levi form has at least $n-q$ positive eigenvalues or at least $q+1$ negative eigenvalues at each boundary point, there are natural isomorphisms between the $(p,q)$ Dolbeault cohomology groups defined by means of $C^\infty$ up to the boundary differential forms on $D$ and the (finite-dimensional) spaces of harmonic $(p,q)$-forms on $D$ determined by the corresponding complex Laplace operator. In the present paper, using Kohn’s technique, we give a similar description of the $(p,q)$ Dolbeault cohomology groups of spaces of differential forms taking values in certain (possibly infinite-dimensional) holomorphic Banach vector bundles on $D$. We apply this result to compute the $(p,q)$ Dolbeault cohomology groups of some regular coverings of $D$ defined by means of $C^\infty$ forms constrained along fibres of the coverings.
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 32A38, 32K99
  • Retrieve articles in all journals with MSC (2010): 32A38, 32K99
Additional Information
  • A. Brudnyi
  • Affiliation: Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada
  • MR Author ID: 292684
  • Email:
  • D. Kinzebulatov
  • Affiliation: The Fields Institute, 222 College Street, Toronto, Ontario M5T 3J1, Canada
  • Email:
  • Received by editor(s): March 5, 2014
  • Received by editor(s) in revised form: November 4, 2014, and December 16, 2014
  • Published electronically: February 12, 2016
  • Additional Notes: The authors’ research was partially supported by NSERC
  • © Copyright 2016 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 369 (2017), 167-186
  • MSC (2010): Primary 32A38, 32K99
  • DOI:
  • MathSciNet review: 3557771