Timeline for Approximating homeomorphisms of 2-disk by diffeomorphisms
Current License: CC BY-SA 4.0
8 events
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| Jan 12, 2022 at 8:32 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
replaced the link to the arXiv front end; see https://meta.mathoverflow.net/questions/5124/is-it-time-to-replace-links-to-the-ucdavis-arxiv-frontend
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| Jun 15, 2014 at 2:31 | history | edited | Igor Belegradek | CC BY-SA 3.0 |
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| Jun 12, 2014 at 15:31 | comment | added | Misha | Igor: Yes, it is easy to approximate Beltrami differentials (using convolutions or any other method you like); then use continuity of dependence of solution of Beltrami equations on the parameters. | |
| Jun 12, 2014 at 14:44 | comment | added | Igor Belegradek | @Misha: for the second step I gather you suggest to smooth the dilatation of PL homeomorphism say via convolution, so that the solutions of the Beltrami equation are smooth approximations of the PL homeomorphisms? | |
| Jun 12, 2014 at 5:30 | comment | added | Igor Belegradek | Looks like the PL approximation is proved in "Uniform PL approximations of isotopies and extending PL isotopies in low dimensions" by Hamstrom, Theorem 6, available online at sciencedirect.com/science/article/pii/0001870876900207. | |
| Jun 12, 2014 at 3:06 | comment | added | Misha | Igor: maybe you can do it in two steps. First construct PL approximation maybe by imitating Munkres. Then use qc nature of PL homeos (Beltrami equation) to find smooth approximation. The second step is easy. | |
| Jun 12, 2014 at 0:48 | history | edited | Igor Belegradek | CC BY-SA 3.0 |
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| Jun 12, 2014 at 0:34 | history | asked | Igor Belegradek | CC BY-SA 3.0 |