2024/09/16 by Włodzimierz Zwonek, Zwonek, Włodzimierz
Mathematics · #Rings, Modules, and Algebras #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2409.10700
Motivated by recent papers \citeFor-Rong 2021 and \citeNg-Rong 2024 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.