Timeline for Motivation behind the parabolic metric
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 30 at 19:53 | vote | accept | BigbearZzz | ||
| Jan 6, 2018 at 21:28 | answer | added | Alex M. | timeline score: 6 | |
| Jan 6, 2018 at 20:31 | comment | added | BigbearZzz | One of the books that use this metric is Roger Moser's "partial regularity for harmonic maps and related problems". | |
| Jan 6, 2018 at 20:29 | comment | added | BigbearZzz | @PiyushGrover It's just the square root there, maybe saying "$2-$dimensions" might not be the best wording. Perhaps I should just ask "why do we want the square root sign there"? | |
| Jan 6, 2018 at 20:25 | comment | added | Piyush Grover | Can you give a reference ? What makes it seem like time is 2D in the formula you wrote ? | |
| Jan 6, 2018 at 20:17 | comment | added | BigbearZzz | @AlexM. That's an interesting observation, thanks! | |
| Jan 6, 2018 at 20:15 | comment | added | Alex M. | I don't know the answer, but the prototypical parabolic equation is the heat equation $(\partial _t - \Delta) u = 0$, where time carries an order-$1$ derivative, while space carries an order-$2$ one, so that one needs to "square" the time derivative to get the same order as the space one. A similar thing seems to happen in your formula. Of course, this is merely an intuition, not an answer. | |
| Jan 6, 2018 at 20:11 | history | asked | BigbearZzz | CC BY-SA 3.0 |