Timeline for Average of the sum of dirac measures
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 29, 2021 at 10:38 | comment | added | mlk | @PierrePC I am not really familiar with sphere packings either, apart from knowing that people study them, but it turns out a general idea about them is enough to finish the proof. I edited my answer to that respect. | |
| Jan 29, 2021 at 0:21 | history | edited | Totoro | CC BY-SA 4.0 |
added 5 characters in body
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| Jan 29, 2021 at 0:19 | comment | added | Totoro | @mlk Sorry for the ambiguity, the "maximal" means "maximal number of points". | |
| Jan 28, 2021 at 23:21 | comment | added | Pierre PC | @mlk I was thinking the same thing, although I am not sure I could work out the details myself; I am not familiar with sphere packings. Maybe the OP can tell us which variant they are interested in. | |
| Jan 28, 2021 at 21:04 | comment | added | mlk | @PierrePC I believe in that case the answer should be yes, though the proof might be a bit technical. But you should be able to show by contradiction that inside any ball $B_\delta$ (with $\delta \ll 1$, so that we can ignore curvature) and $\epsilon \ll \delta$, the number of points needs to be close to the one expected from the related optimal sphere packing. This then gives you that $m_\epsilon(B_\delta) \to c |B_\delta|$ (possibly up to another small error) with the same constant everywhere, which I believe proves the assertion. | |
| Jan 28, 2021 at 17:47 | comment | added | Pierre PC | I'd be interested in the answer for the case where the maximality of $\mathcal B_\varepsilon$ is meant in terms of number of points. | |
| Jan 28, 2021 at 16:39 | answer | added | mlk | timeline score: 4 | |
| Jan 28, 2021 at 8:40 | history | asked | Totoro | CC BY-SA 4.0 |