Timeline for Gromov-Hausdorff limits of 2-dimensional Riemannian surfaces
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| May 2, 2016 at 11:26 | history | edited | Mikhail Katz | CC BY-SA 3.0 |
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| Apr 19, 2016 at 17:08 | history | edited | Mikhail Katz | CC BY-SA 3.0 |
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| Apr 19, 2016 at 17:07 | comment | added | Mikhail Katz | @sva, the argument only works for hyperbolic surfaces (hence genus at least 2) since otherwise Gauss-Bonnet does not give a lower bound for the area. | |
| Apr 19, 2016 at 15:37 | comment | added | Mikhail Katz | The systole is the least length of a noncontractible loop on the surface $M$. The filling radius of $M$ is defined as the least epsilon such that the inclusion of $M$ in its epsilon-neighborhood sends the fundamental homology class of $M$ to zero. Here the embedding is in the space of bounded functions on $M$ which sends a point to the distance function from that point. Actually this stage can be bypassed and one can show directly an inequality between the systole and the $(n-1)$-diameter. | |
| Apr 19, 2016 at 15:31 | comment | added | asv | Systole and filling radius. Also apparently you use their relation to the Gromov-Hausdorff distance (to a graph?). BTW in your statement should one add the condition that the genus of the surfaces in at least 2? | |
| Apr 19, 2016 at 15:26 | comment | added | Mikhail Katz | @sva, which concepts are you not familiar with? | |
| Apr 19, 2016 at 15:26 | history | edited | Mikhail Katz | CC BY-SA 3.0 |
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| Apr 19, 2016 at 15:24 | comment | added | asv | Unfortunately I am unfamiliar with some of the background you use. What statement exactly you proved? | |
| Apr 19, 2016 at 13:09 | history | answered | Mikhail Katz | CC BY-SA 3.0 |