Timeline for A dichotomy for everywhere differentiable eikonal functions
Current License: CC BY-SA 4.0
20 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Nov 19 at 11:07 | history | bounty ended | Nate River | ||
| S Nov 19 at 11:07 | history | notice removed | Nate River | ||
| Nov 17 at 15:56 | vote | accept | Nate River | ||
| Nov 17 at 15:54 | vote | accept | Nate River | ||
| Nov 17 at 15:56 | |||||
| Nov 17 at 15:07 | answer | added | Scott Armstrong | timeline score: 1 | |
| S Nov 17 at 13:50 | history | bounty started | Nate River | ||
| S Nov 17 at 13:50 | history | notice added | Nate River | Draw attention | |
| Sep 23 at 13:27 | history | edited | Nate River | CC BY-SA 4.0 |
edited title
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| Sep 23 at 12:54 | vote | accept | Nate River | ||
| Nov 17 at 13:01 | |||||
| Aug 28 at 2:51 | comment | added | Nate River | Ah indeed, Theorem 4.1 in the paper above is an example. | |
| Aug 28 at 1:59 | answer | added | Richard Montgomery | timeline score: 4 | |
| Aug 27 at 21:18 | comment | added | Nate River | The paper Infinite games, Banach space geometry and the Eikonal equation seems to construct a potential example of such functions. @IosifPinelis | |
| Aug 26 at 14:19 | comment | added | Nate River | @DaveLRenfro Well that looks just delightful… | |
| Aug 26 at 14:14 | comment | added | Dave L Renfro | Weil's gradient problem seems to be relevant. | |
| Aug 26 at 13:05 | comment | added | Leo Moos | Whoops, I'd deleted my comment in the meantime. For the record, here is what the original comment said: "Isn't there the trick with the derivative $f'$ of a (not necessarily $C^1$) function $f: \mathbf{R} \to \mathbf{R}$ retaining the intermediate value property?" | |
| Aug 26 at 13:03 | comment | added | Nate River | @LeoMoos right, but that only works along lines. In $\mathbb R^n$ you get a path integral, along which the derivative can take values other than $1$ even though $|\nabla f| = 1$ a.e. | |
| Aug 26 at 13:02 | comment | added | Nate River | Though I guess the nonexistence of such functions would be an even stronger claim than mine. | |
| Aug 26 at 13:01 | comment | added | Nate River | @IosifPinelis I do not even have that… | |
| Aug 26 at 12:50 | comment | added | Iosif Pinelis | Do you have an example of a function $f\colon\mathbb R^n \to \mathbb R$ that is everywhere differentiable, with $|\nabla f| = 1$ almost everywhere but not everywhere? | |
| Aug 26 at 12:14 | history | asked | Nate River | CC BY-SA 4.0 |