D. Zaitsev & F. Bracci 'Boundary jets of holomorphic maps between strongly pseudoconvex domains' in Journal of Functional Analysis, 254, (6), 2008, pp 1449-1466
Journal of Functional Analysis 254 6
We study jets of germs of holomorphic maps between two strongly pseudoconvex domains under the condition that the image of one domain is contained into the other and a given boundary point is (non-tangentially) mapped to a given boundary point. We completely characterize the (non-tangential) 1-jets. Moreover we give algebraic inequalities (in terms of Chern-Moser normal forms up to a certain low order) for the admissible germs with a given 1-jet. Also, we prove a rigidity result which says that there exists a germ tangent to the Identity (in some local charts) if and only if the two domains are tangent up to weighted order five.
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