Published online by Cambridge University Press: 22 January 2016
One of the main problems in complex analysis has been to determine when two open sets D1, D2 in Cn are biholomorphically equivalent. In  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 B 2. Recently Burns, Shnider and Wells  (cf. also Chern-Moser ) 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.
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