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Deformations and equitopological deformations of strongly pseudoconvex manifolds

Published online by Cambridge University Press:  22 January 2016

Stephen S.-T. Yau
Stephen S.-T. Yau*
Affiliation:
Department of Mathematics, Harvard University, Cambridge, Mass. 02138, Department of Mathematics, University of Illinois at Chicago Circle, Chicago, Illinois 60680
*
Department of Mathematics, Princeton University, Princeton, N.J. 08540
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One of the main problems in complex analysis has been to determine when two open sets D1, D2 in Cn are biholomorphically equivalent. In [26] Poincaré studied perturbations of the unit ball B2 in C2 of a particular kind, and found necessary and sufficient conditions on a first order perturbation that the perturbed domain be biholomorphically equivalent to B2. Recently Burns, Shnider and Wells [7] (cf. also Chern-Moser [9]) have studied the deformations of strongly pseudoconvex manifolds. They proved that there is no finite-dimensional deformation theory for M if one keeps track of the boundary.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 82 , June 1981 , pp. 113 - 129
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1981

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