Timeline for Are there $n$ points dividing a compact Riemannian manifold into equal regions?
Current License: CC BY-SA 4.0
10 events
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| Jan 4, 2023 at 16:32 | history | edited | LSpice | CC BY-SA 4.0 |
Answer to what?; link to comment; capitalise title as in body
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| Jan 4, 2023 at 13:46 | history | edited | Saúl RM | CC BY-SA 4.0 |
In the remark we need the manifold to be complete, it's not enough with finite volume.
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| Jan 4, 2023 at 13:38 | history | edited | Saúl RM | CC BY-SA 4.0 |
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| Jan 1, 2023 at 18:53 | history | edited | Saúl RM | CC BY-SA 4.0 |
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| Jan 1, 2023 at 18:47 | history | edited | Saúl RM | CC BY-SA 4.0 |
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| Jan 1, 2023 at 18:12 | history | edited | Saúl RM | CC BY-SA 4.0 |
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| Jan 1, 2023 at 18:05 | comment | added | Saúl RM | If $M$ is the flat $m$-torus the statement is true for any $n$, because we can just get one factor $\mathbb{S}^1$ of the torus and place $n$ evenly spaced points in it. The same works for the $m$-sphere, in general if you have a group acting on $M$ by isometries with an orbit formed by $n$ points you can choose those $n$ points. But of course this need not be the case. | |
| Jan 1, 2023 at 16:16 | comment | added | Will Jagy | Do you know how this works in the flat 2-torus? I've been drawing pictures on graph paper, torus as quotient | |
| Dec 31, 2022 at 17:39 | comment | added | Anthony Quas | For what it’s worth, the regions you are talking about are called Voronoi cells. | |
| Dec 31, 2022 at 17:27 | history | asked | Saúl RM | CC BY-SA 4.0 |