Timeline for Smoothness of distance function in Riemannian Manifolds
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 3, 2020 at 13:29 | comment | added | popoolmica | What can be said about the smoothness of $d(x,y)$ as a function of $x$? | |
| May 22, 2019 at 16:31 | answer | added | Jan Bohr | timeline score: 13 | |
| Apr 15, 2010 at 5:02 | vote | accept | Mauricio | ||
| Apr 14, 2010 at 16:45 | comment | added | Mauricio | Spencer. You are right. I have corrected the post. | |
| Apr 14, 2010 at 16:37 | history | edited | Mauricio | CC BY-SA 2.5 |
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| Apr 14, 2010 at 10:34 | comment | added | Spencer | I know we all know what you're talking about but presumeably you want $\mathbb{R}$ as your codomain rather than the manifold. | |
| Apr 14, 2010 at 9:45 | answer | added | Sergei Ivanov | timeline score: 65 | |
| Apr 14, 2010 at 5:04 | comment | added | Jason DeVito - on hiatus | One often looks at $d^2$ instead of $d$. This at least fixes the smoothness issues along the diagonal mentioned by Ryan. Still, on any comapct manifold, $d^2$ will necessarily fail to be smooth at some points. | |
| Apr 14, 2010 at 4:05 | answer | added | Mariano Suárez-Álvarez | timeline score: 34 | |
| Apr 14, 2010 at 4:04 | comment | added | Ryan Budney | Similarly, it's not smooth along the diagonal $\{(x,x) : x \in \mathcal{M}\}$ | |
| Apr 14, 2010 at 4:02 | comment | added | Ryan Budney | It's never smooth for a compact manifold. Consider a diameter -- the maximum of the function. It's not smooth there. For example, consider $S^n$. You get cone-type singularities. | |
| Apr 14, 2010 at 3:46 | history | asked | Mauricio | CC BY-SA 2.5 |