On the boundary rigidity phenomenon for automorphisms of domains in ℂⁿ

Coupet, Bernard; Sukhov, Alexander

doi:10.1090/S0002-9939-96-03573-3

On the boundary rigidity phenomenon for automorphisms of domains in $\mathbb {C}^n$
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by Bernard Coupet and Alexander Sukhov PDF

Proc. Amer. Math. Soc. 124 (1996), 3371-3380 Request permission

Abstract:

We prove that a piecewise smoothly bounded strictly pseudoconvex domain with a non–compact automorphism group is biholomorphic to the ball. A boundary version of the Schwarz lemma for automorphisms of such a domain is settled.

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