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Burns-Krantz rigidity in non-smooth domains

Part of: Holomorphic functions of several complex variables

Published online by Cambridge University Press:  18 March 2025

Włodzimierz Zwonek Open the ORCID record for Włodzimierz Zwonek [Opens in a new window]
Włodzimierz Zwonek*
Affiliation:
Institute of Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, Kraków 30–348, Poland
*
e-mail: [email protected]
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Abstract

Motivated by recent papers [11] and [19] we prove a boundary Schwarz lemma (Burns-Krantz rigidity type theorem) for non-smooth boundary points of the polydisc and symmetrized bidisc. Basic tool in the proofs is the phenomenon of invariance of complex geodesics (and their left inverses) being somehow regular at the boundary point under the mapping satisfying the property as in the Burns-Krantz rigidity theorem that lets the problem reduce to one dimensional problem. Additionally, we make a discussion on bounded symmetric domains and suggest a way to prove the Burns-Krantz rigidity type theorem in these domains that however cannot be applied for all bounded symmetric domains.

Keywords

Burns-Krantz rigidity propertypolydiscsymmetrized bidiscLempert theorem

MSC classification

Primary: 32A40: Boundary behavior of holomorphic functions
Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 10
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

Research was partially supported by the Sheng grant no. 2023/48/Q/ST1/00048 of the National Science Center, Poland.

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