Timeline for When is the cut locus a finite tree?
Current License: CC BY-SA 4.0
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| Nov 12 at 18:04 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
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| Feb 21, 2023 at 13:16 | history | edited | Leo Moos | CC BY-SA 4.0 |
fixed a typo; added italics for emphasis
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| Feb 20, 2023 at 19:35 | history | edited | Leo Moos | CC BY-SA 4.0 |
clarified question
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| S Feb 20, 2023 at 13:15 | history | bounty started | Leo Moos | ||
| S Feb 20, 2023 at 13:15 | history | notice added | Leo Moos | Draw attention | |
| Feb 20, 2023 at 13:15 | history | edited | Leo Moos | CC BY-SA 4.0 |
clarified question
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| Feb 20, 2023 at 13:05 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Feb 1, 2021 at 14:16 | comment | added | JHM | The pathological smooth shapes (relative to cut loci) are those with constant curvature, which is everywhere destroyed by generic perturbations. But the pathological continuous curves are much wilder, e.g. sin(1/x) graphs, and i avoid them. | |
| Feb 1, 2021 at 13:34 | comment | added | Leo Moos | @user142382 I should have specified that the perturbation in question ought to be in the smooth category: the perturbed curve should remain regular, which excludes the piecewise linear curves that you suggest. | |
| Jan 31, 2021 at 19:38 | comment | added | Leo Moos | @MattF. That's a fortuitous coincidence - I would certainly welcome their input! | |
| Jan 31, 2021 at 18:15 | comment | added | user44143 | Both authors are on MO -- perhaps either DmitriPanov or @AntonPetrunin will comment! | |
| Jan 30, 2021 at 12:06 | answer | added | JHM | timeline score: 0 | |
| Jan 29, 2021 at 22:24 | history | edited | Leo Moos | CC BY-SA 4.0 |
edited title
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| Jan 29, 2021 at 20:43 | comment | added | Leo Moos | @JosephO'Rourke Thank you for this, some of the references could be relevant, although I didn't see any that look directly applicable. | |
| Jan 29, 2021 at 20:23 | comment | added | user142382 | Possibly this is wrong, but: Isn't the cut locus a finite graph if the curve $\gamma$ is piecewise linear, and can't this be arranged after an arbitrarily small perturbation? | |
| Jan 29, 2021 at 16:38 | comment | added | Joseph O'Rourke | Not sure, but there may be relevant citations in this paper: Itoh, Jin-ichi, and Costin Vîlcu. "Every graph is a cut locus." Journal of the Mathematical Society of Japan 67, no. 3 (2015): 1227-1238. arXiv abs. | |
| Jan 29, 2021 at 15:11 | history | asked | Leo Moos | CC BY-SA 4.0 |