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Conformal Geometry and Dynamics

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Winding numbers and full extendibility in holomorphic motions


Author: Yunping Jiang
Journal: Conform. Geom. Dyn. 24 (2020), 109-117
MSC (2010): Primary 32G15; Secondary 30C99, 37F30
DOI: https://doi.org/10.1090/ecgd/351
Published electronically: May 26, 2020
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Abstract: We construct an example of a holomorphic motion of a five-point subset of the Riemann sphere over an annulus such that it satisfies the zero winding number condition but is not fully extendable.


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Additional Information

Yunping Jiang
Affiliation: Department of Mathematics, Queens College of the City University of New York, Flushing, New York 11367-1597; Department of Mathematics, Graduate Center of the City University of New York, New York, New York 10016
Email: yunping.jiang@qc.cuny.edu

DOI: https://doi.org/10.1090/ecgd/351
Keywords: Holomorphic motions, fully extendable, connected one-dimensional hyperbolic complex manifold, the zero winding number condition
Received by editor(s): February 6, 2020
Published electronically: May 26, 2020
Additional Notes: This material is based upon work supported by the National Science Foundation. It is also partially supported by a collaboration grant from the Simons Foundation (grant number 523341) and PSC-CUNY awards.
Article copyright: © Copyright 2020 American Mathematical Society