Timeline for About the metric and embedding of sphere
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| May 24, 2020 at 21:34 | comment | added | Quarto Bendir | Pogorelov showed the following more general result. For a general metric on $S^2$, if the Gaussian curvature is strictly greater than $-\kappa$ for a nonnegative number $\kappa$, then the metric can be isometrically embedded into the simply-connected complete space form of curvature $-\kappa$. | |
| May 13, 2020 at 16:26 | comment | added | Deane Yang | A little clarification: When the Gauss curvature is positive, then it's known as the Weyl problem and was proved independently. by Nirenberg and Pogorelov. For nonnegative Gauss curvature, there is a result by Guan and Li, projecteuclid.org/euclid.jdg/1214454874. If the Gauss curvature is negative somewhere, then nothing is known. | |
| May 13, 2020 at 15:28 | history | answered | Ben McKay | CC BY-SA 4.0 |