Timeline for Lower estimate on the covariant derivative of a section of a curved vector bundle
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Feb 17, 2023 at 4:32 | comment | added | Deane Yang | I'm pretty sure a pointwise bound of the form $|\nabla s| \le C$, where $C$ depends only on the curvature, is straightforward. But, as you say, $s$ could be oscillating, so a bound such as $|\nabla s| \ge C$, where $C$ depends only on the curvature seems unlikely to me. | |
| Feb 16, 2023 at 18:39 | history | became hot network question | |||
| Feb 16, 2023 at 16:24 | comment | added | Sebastian Goette | @DeaneYang Can you explain, please? Do you mean "upper bound on $\nabla s$"? Note that $s$ could be oscillating. Also, do you mean a sign assumption on the curvature of $(M,g)$? I don't see an obvious sign convention for the curvature of $(E,\nabla)$ here. | |
| Feb 16, 2023 at 16:03 | comment | added | Deane Yang | An upper bound should be straightforward but a lower bound probably requires a sign assumption on the curvature. | |
| Feb 16, 2023 at 14:56 | answer | added | MyShepherd | timeline score: 4 | |
| Feb 16, 2023 at 10:32 | history | asked | Sebastian Goette | CC BY-SA 4.0 |