Timeline for Packing a Riemannian manifold with disjoints balls
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 7, 2022 at 22:34 | answer | added | Saúl RM | timeline score: 1 | |
| Dec 7, 2022 at 16:15 | history | edited | YCor |
edited tags
|
|
| Dec 7, 2022 at 16:14 | history | edited | Piotr Hajlasz | CC BY-SA 4.0 |
added 20 characters in body
|
| Apr 7, 2020 at 4:45 | comment | added | Moishe Kohan | @Pii_jhi: Of course, I meant closed balls, as in your question. In all packing constructions I know, the residual set has positive H.D. | |
| Apr 5, 2020 at 10:26 | comment | added | Pii_jhi | The residual set will contain the boundary of the ball (if we consider open balls), so it will be of Hausdorff dimension $d-1$ at least and I think it has to be strictly greater than $d-1$. In the case of Apollonian packing, which feels close to an"optimal" packing, has Hausdorff dimension $\simeq 1.3$.. | |
| Apr 5, 2020 at 8:49 | comment | added | Moishe Kohan | In the case of $E^n$'s, such packings do exist. For instance, Apollonian packing does the job for the Euclidean plane. Not sure what happens if one requires zero Hausdorff dimension of the residual set. | |
| Apr 5, 2020 at 8:20 | history | edited | Pii_jhi | CC BY-SA 4.0 |
I forgot the disjoint hypothesis
|
| Apr 5, 2020 at 8:16 | comment | added | Pii_jhi | I forgot the disjoint hypothesis in my question.. | |
| Apr 5, 2020 at 8:15 | history | edited | Pii_jhi | CC BY-SA 4.0 |
I forgot the disjoint hypothesis
|
| Apr 4, 2020 at 21:14 | comment | added | Kevin Casto | It seems to me we should be able to actually cover $M$ by a countable collection of closed (compact) balls. | |
| Apr 4, 2020 at 21:11 | answer | added | Ryan Vaughn | timeline score: 1 | |
| Apr 4, 2020 at 19:31 | history | asked | Pii_jhi | CC BY-SA 4.0 |