Timeline for Finding the shortest curve that is at distance $\epsilon$ of every point of a surface
Current License: CC BY-SA 3.0
3 events
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| Jan 16, 2017 at 16:42 | comment | added | Victor Protsak | My point was that you need to be much more careful with formulating your problem. The basic phenomenon (already for a unit disk and $\epsilon $ close to and less than 1) is that various optimal sets tend to be disconnected. Depending on the type of $\gamma $ you stipulate (e.g. Peano continuum or unicursal graph), possible solutions, if they exist, can vary greatly. I agree that, logically speaking, none of this precludes the pure existence in a specific class of $\gamma $; as for explicit construction, I am very pessimistic for the reasons outlined. Best wishes, Victor. | |
| Jan 16, 2017 at 9:10 | comment | added | LCO | Thank you for you answer, but I don't see how this answers (negatively) the question. By curve, i do mean continuous (and even smooth). I don't see how the fact that there is an optimal set that is not a curve, imply that there is no curve that goes near every point at distance $\leq \epsilon$ , and such that any other curve satisfying this, will be longer. | |
| Jan 16, 2017 at 2:02 | history | answered | Victor Protsak | CC BY-SA 3.0 |