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Two-point distortion bounds for biholomorphic mappings of the ball in Cn
| Content Provider | Semantic Scholar |
|---|---|
| Author | Muir, Jerry R. |
| Copyright Year | 2014 |
| Abstract | Abstract Lower and upper two-point distortion bounds for families F of biholomorphic mappings on the unit ball B of C n are given in terms of the (trace) order of the linear-invariant family generated by F , bounds on ratios involving the derivative and Jacobian of the mappings in F , and the Caratheodory distance on B . (By two-point distortion bounds, we mean estimates on ‖ f ( b ) − f ( a ) ‖ for a , b ∈ B and f ∈ F .) This immediately results in growth bounds for such mappings. A contrast is drawn between these bounds and two-point distortion bounds in terms of the norm order of the generated linear-invariant family. As part of our work, we develop a lower distortion bound for automorphisms of B that may be of independent interest. |
| Starting Page | 23 |
| Ending Page | 41 |
| Page Count | 19 |
| File Format | PDF HTM / HTML |
| DOI | 10.1016/j.jmaa.2014.02.059 |
| Alternate Webpage(s) | https://royaldrive.scranton.edu/Users/muirj2/Web/Articles/distortion.pdf |
| Alternate Webpage(s) | https://doi.org/10.1016/j.jmaa.2014.02.059 |
| Volume Number | 417 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
