Timeline for Are all $C^1$ arcs tame?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Sep 21, 2011 at 3:50 | vote | accept | CommunityBot | ||
| Sep 20, 2011 at 20:19 | comment | added | George Lowther | Alternatively, by deforming locally on sections on which its direction changes by less than 180deg, you can make it $C^\infty$, and constant derivative on the initial segment. Then, extend $p^\prime$ locally to a smooth vector field vanishing away from $p$. Moving along the flow of the vector field, you can shorten $p$ to a straight line segment. | |
| Sep 20, 2011 at 20:13 | answer | added | Sergei Ivanov | timeline score: 3 | |
| Sep 20, 2011 at 20:05 | comment | added | George Lowther | The answer has to be yes. You can deform $p$ to $p^\prime = p\vert\_{[0,t^\prime]}$ for any $0 < t^\prime < t$. Choosing $t^\prime$ small enough so that the direction of $p^\prime$ changes by less than 180deg, then straighten it out. | |
| Sep 20, 2011 at 19:46 | history | edited | user5810 | CC BY-SA 3.0 |
added injectivity
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| Sep 20, 2011 at 19:32 | history | asked | user5810 | CC BY-SA 3.0 |