Rigidity of holomorphic mappings and a new Schwarz lemma at the boundary

Burns, Daniel M.; Krantz, Steven G.

doi:10.1090/S0894-0347-1994-1242454-2

Rigidity of holomorphic mappings and a new Schwarz lemma at the boundary
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by Daniel M. Burns and Steven G. Krantz

J. Amer. Math. Soc. 7 (1994), 661-676

DOI: https://doi.org/10.1090/S0894-0347-1994-1242454-2

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Abstract:

A rigidity theorem for holomorphic mappings, in the nature of the uniqueness statement of the classical one-variable Schwarz lemma, is proved at the boundary of a strongly pseudoconvex domain. The result reduces to an interesting, and apparently new, result even in one complex dimension. The theorem has a variety of geometric and analytic interpretations.

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