Timeline for Nonvanishing of Jacobians implies global injectivity?
Current License: CC BY-SA 3.0
8 events
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| May 1, 2023 at 12:32 | comment | added | The Amplitwist |
The link to springerlink.com is broken, but the article can be found at doi:10.1007/BF01360282 or at EuDML (Zbl 0158.04903).
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| Aug 17, 2012 at 16:22 | answer | added | Marc Chamberland | timeline score: 1 | |
| May 12, 2012 at 17:33 | comment | added | Syang Chen | @Misha: Thank you. Zorich's theorem and the results on en.wikipedia.org/wiki/Quasiregular_map are very impressive. Unfortunately the maps I am concerned with are not quasiregular. Their Jocobians collapse when two coordinates coincide whereas their gradients do not. | |
| May 7, 2012 at 4:34 | comment | added | Misha | @Syang: You may also want to take a look at Zorich Theorem (en.wikipedia.org/wiki/Zorich's_theorem): If $f: {\mathbb R}^n\to {\mathbb R}^n$ is a locally-injective quasiregular map, then, for $n\ge 3$, the map $f$ is a homeomorphism. A smooth map $f$ is $K$-quasiregular if $||Df(x)||^n\le K |J_f(x)|$ for all $x\in {\mathbb R}^n$. The assumptions are somewhat different from the ones you are asking, but the conclusion is the same. | |
| Feb 13, 2012 at 15:44 | answer | added | BS. | timeline score: 4 | |
| Feb 13, 2012 at 7:04 | history | edited | Syang Chen | CC BY-SA 3.0 |
deleted 74 characters in body; edited tags; edited title
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| Feb 12, 2012 at 4:12 | history | edited | Syang Chen | CC BY-SA 3.0 |
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| Feb 12, 2012 at 4:05 | history | asked | Syang Chen | CC BY-SA 3.0 |