Burns-Krantz rigidity in non-smooth domains
Canadian mathematical bulletin, Tome 68 (2025) no. 4, pp. 1037-1046
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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.
Mots-clés :
Burns-Krantz rigidity property, polydisc, symmetrized bidisc, Lempert theorem
Zwonek, Włodzimierz. Burns-Krantz rigidity in non-smooth domains. Canadian mathematical bulletin, Tome 68 (2025) no. 4, pp. 1037-1046. doi: 10.4153/S0008439525000311
@article{10_4153_S0008439525000311,
author = {Zwonek, W{\l}odzimierz},
title = {Burns-Krantz rigidity in non-smooth domains},
journal = {Canadian mathematical bulletin},
pages = {1037--1046},
year = {2025},
volume = {68},
number = {4},
doi = {10.4153/S0008439525000311},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439525000311/}
}
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