Timeline for Can you cover a genus a billion hyperbolic surface with 15 balls?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Dec 3, 2023 at 17:20 | comment | added | Moishe Kohan | Thus, both radii grow as $\log(n)$. | |
| Dec 3, 2023 at 17:14 | comment | added | Moishe Kohan | @MikhailKatz: Sorry, I am slow. The growth rates of the radii of the disks are, respectively, $arcosh(2n/\pi)$ (for the disk centered at the center of the polygon) and $arcosh(n/\pi)$ (for the disks centered at the vertices of the polygon). I am not yet there with an estimate of the systole. | |
| Nov 29, 2023 at 14:56 | comment | added | Moishe Kohan | @MikhailKatz: I would have to do a calculation for radii. I can offer only an educated guess on systoles (upper bounds which may or may not be sharp). | |
| Nov 29, 2023 at 14:29 | comment | added | Mikhail Katz | @MoisheKohan, What is the order of growth of the radius of these disks that you construct here? Do they grow as constant times $\log g$ or slower? Can one get lower bounds for the systole of these surfaces? | |
| Jan 29, 2021 at 18:42 | comment | added | Will Sawin | I suggest you post your modified question as its own question... | |
| Jan 29, 2021 at 17:27 | comment | added | Moishe Kohan | @WillSawin: I am not sure about that. As far as I am concerned, it would be interesting to get 3 disks for all closed oriented surfaces of negative Euler characteristic: I could do this in the oriented case if $\chi$ is divisible by 3. If you have a construction in the general oriented case, consider posting it as an answer. | |
| Jan 29, 2021 at 17:05 | comment | added | biringer | I take great pride in submitting a MO question that has many quick elementary answers! 🥳 | |
| Jan 29, 2021 at 16:45 | history | edited | Moishe Kohan | CC BY-SA 4.0 |
added 326 characters in body
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| Jan 29, 2021 at 15:13 | comment | added | Will Sawin | Nice! I think one can do this also with three discs of the same radius by taking three copies of a hyperbolic $4n+2$-gon with vertex angle $2\pi/3$, gluing them to a surface, and taking the discs in which each $4n+2$-gon is inscribed. | |
| Jan 29, 2021 at 13:58 | comment | added | Moishe Kohan | @biringer: You are welcome! The nontrivial question, I think, is about higher-dimensional (say, dimension $>100$) hyperbolic manifolds. | |
| Jan 29, 2021 at 12:33 | comment | added | biringer | You know, this is great, and probably the first thing I should have tried, but for some reason it’s still surprising to me from the way I was looking at it before. In any case, many thanks, I appreciate it! | |
| Jan 29, 2021 at 12:18 | vote | accept | biringer | ||
| Jan 29, 2021 at 9:30 | history | answered | Moishe Kohan | CC BY-SA 4.0 |