Timeline for Smoothness of signed distance function to a hypersurface
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 12 at 14:33 | comment | added | Anton Petrunin | If $d$ is $C^1$ in a neighborhood of $\Sigma$, then normal curvatures of $\Sigma$ are bounded. Therefore $\Sigma$ should be at least $C^2$. | |
| Dec 30, 2023 at 9:35 | comment | added | Nate River | In Chapter 6 of Lee's Riemannian Manifolds book, he proves that $d$ is $C^\infty$ near $\Sigma$ under the assumption that $\Sigma$ is $C^\infty$. (Theorem 6.40) Perhaps the proof can be generalised. | |
| Dec 29, 2023 at 21:02 | history | asked | gaoqiang | CC BY-SA 4.0 |