We prove a rigidity theorem which generalizes a result due to Burns and Krantz (see[3]) for holomorphic self-maps in the unit disk of the complex plane. Essentially, we found that some conditions on the (boundary) Schwarzian derivative 0f a holomorphic self-map at specific points of the boundary of the disk may be sufficient to conclude that a map is a completely determined rational map.
Tauraso, R., Vlacci, F. (2001). Rigidity at the Boundary for Holomorphic Self-Maps of the Unit Disc. COMPLEX VARIABLES THEORY AND APPLICATION, 45(2), 151-165 [10.1080/17476930108815374].
Rigidity at the Boundary for Holomorphic Self-Maps of the Unit Disc
TAURASO, ROBERTO;
2001-01-01
Abstract
We prove a rigidity theorem which generalizes a result due to Burns and Krantz (see[3]) for holomorphic self-maps in the unit disk of the complex plane. Essentially, we found that some conditions on the (boundary) Schwarzian derivative 0f a holomorphic self-map at specific points of the boundary of the disk may be sufficient to conclude that a map is a completely determined rational map.File in questo prodotto:
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