Rigidity of CR maps between Shilov boundaries of bounded symmetric domains

Abstract

Our goal is to establish what seems to be the first rigidity result for CR embeddings between Shilov boundaries of bounded symmetric domains of higher rank. The result states that any such CR embedding is the standard linear embedding up to CR automorphisms. Our basic assumption extends precisely the well-known optimal bound for the rank one case. There are no other restrictions on the ranks, in particular, the difficult case when the target rank is larger than the source rank is also allowed.

References in corpus (2)

• A new gap phenomenon for proper holomorphic mappings from B^n into B^N
• Super-rigidity for CR embeddings of real hypersurfaces into hyperquadrics

Cited by in corpus (7)

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• Regularity of CR-mappings into Levi-degenerate hypersurfaces
• On local holomorphic maps preserving invariant (p,p)-forms between bounded symmetric domains
• Complexity of holomorphic maps from the complex unit ball to classical domains