Timeline for Differentiability of signed distance function to hypersurfaces without compactness
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 15, 2023 at 23:31 | comment | added | Otis Chodosh | you can do something similar where two sheets of M get close together near infinity. Or e.g a spiraling curve. | |
| Mar 15, 2023 at 22:37 | comment | added | Jo' | Thank you, but I want to fix $M$. So, given this particular $M$, can I find a uniform $\epsilon>0$ such that the signed distance is $C^2$ for all $y\in \{z:d(z,M) <\epsilon\}$? | |
| Mar 15, 2023 at 21:52 | comment | added | Otis Chodosh | Take $U = \mathbb{R}^3$ and $M= \{z=0\} \cup \{z=\epsilon\}$. You cannot obtain a uniform such estimate as $\epsilon\to 0$ (the distance function is not $C^2$ at $z=\epsilon/2$). | |
| Mar 15, 2023 at 20:58 | history | edited | Jo' | CC BY-SA 4.0 |
edited title
|
| S Mar 15, 2023 at 20:51 | review | First questions | |||
| Mar 15, 2023 at 20:53 | |||||
| S Mar 15, 2023 at 20:51 | history | asked | Jo' | CC BY-SA 4.0 |