Timeline for Are geodesics locally minimizing in continuous curves?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 27, 2011 at 18:01 | vote | accept | Sebastian Scholtes | ||
| Jun 27, 2011 at 16:35 | answer | added | Anton Petrunin | timeline score: 6 | |
| Jun 27, 2011 at 15:31 | comment | added | Igor Rivin | To amplify @Charlie's comment: how do you define the length of a curve? If as the limit of piecewise-smooth approximations, then the statement is immediate. If not, you should tell us your definition of length... | |
| Jun 27, 2011 at 13:09 | comment | added | Andreas Blass | I'd think a non-rectifiable continuous curve could naturally be assigned infinite "length" (by using the same supremum of distances as in the definition for rectifiable curves), so that you wouldn't have to worry about them as candidates for minimizing lengths. | |
| Jun 27, 2011 at 12:43 | comment | added | Charlie Frohman | Continuous curves don't neccessarily have a length. Let's add the hypothesis that the curve be rectifiable, also lets assume we are in a complete Riemannian manifold, then the answer is yes. | |
| Jun 27, 2011 at 12:36 | history | asked | Sebastian Scholtes | CC BY-SA 3.0 |