Timeline for Constant Gaussian curvature disks
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 17, 2021 at 3:58 | comment | added | Deane Yang | See math.stackexchange.com/questions/3986936/… for another answer by me. | |
| Jan 17, 2021 at 3:55 | comment | added | Anton Petrunin | @MoisheKohan a Morse-type argument does it. | |
| Jan 17, 2021 at 3:39 | comment | added | Moishe Kohan | This is is same proof as Deane's argument and is similarly incomplete. You have to argue that $i$ is 1-1 (it would suffice to prove injectivity in the boundary). This is not har though. You can use the fact that the teardrop orbifold does not admit a spherical structure. | |
| Jan 16, 2021 at 20:22 | comment | added | Deane Yang | The existence of an isometric immersion of $D$ into $\mathbb{S}^2$ follows, for example, by Bonnet's Theorem, which is stated and proved in Do Carmo's book, Differential geometry of curves and surfaces. | |
| Jan 16, 2021 at 19:59 | comment | added | Deane Yang | I think this and the original question really belong in MSE. I’ve posted a different answer to the original question there. | |
| Jan 16, 2021 at 18:09 | comment | added | Eduardo Longa | @AntonPetrunin why does $\iota:D \to \mathbb{S}^2$ exist? | |
| Jan 16, 2021 at 6:09 | history | edited | Anton Petrunin | CC BY-SA 4.0 |
added 4 characters in body
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| Jan 16, 2021 at 4:25 | comment | added | Deane Yang | @AntonPetrunin, I presume that in the second paragraph, $f(\partial D)$ should be $\iota(\partial D)$. And is saying that it has constant curvature enough? Don't you have to show that the torsion is zero? | |
| Jan 16, 2021 at 3:28 | comment | added | Anton Petrunin | Any reasonable function, say with one maximum and one minimum on the boundary. | |
| Jan 16, 2021 at 3:26 | comment | added | Eduardo Longa | What is $f$ here? | |
| Jan 16, 2021 at 3:24 | history | answered | Anton Petrunin | CC BY-SA 4.0 |