Abstract
We develop an isotopy principle for holomorphic motions. Our main result concerns the extendability of a holomorphic motion h(t,z) of a finite subset E of the Riemann sphere C parameterized by a pointed hyperbolic Riemann surface (X,t0). We prove that if this holomorphic motion has a guiding quasiconformal isotopy, then it can be extended to a new holomorphic motion of E ∪ {p} for any point p in C E that follows the guiding isotopy. The proof gives a canonical way to replace a continuous motion of the (n + 1)-st point by a holomorphic motion while leaving unchanged the given holomorphic motion of the first n points.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Annales Academiae Scientiarum Fennicae Mathematica
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
