Timeline for Busemann-Feller lemma in hyperbolic space
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 8, 2021 at 9:57 | comment | added | Benoît Kloeckner | Note that in $\mathbb{R}^n$, if (1) is true for a compact set $K$ then $K$ must be convex. This is interstingly not true in $\mathbb{H}^n$, where horospheres are not flat. You can see that as several variants of convexity that no longer match (using either geodesic or busemann functions). | |
| Jul 8, 2021 at 6:00 | vote | accept | asv | ||
| Jul 8, 2021 at 3:56 | answer | added | Mohammad Ghomi | timeline score: 7 | |
| Jul 7, 2021 at 14:31 | comment | added | asv | @LeoMoos: to be more precise one should consider everything in open half-sphere rather than sphere. | |
| Jul 7, 2021 at 14:13 | comment | added | Leo Moos | Are you sure about (1) holding in spherical space? If $\pm p \in \mathbf{S}^n$ are antipodal and $D_r(p)$ is a closed disc around $p$, then the nearest points to $-p$ form $\partial D_r(p)$, no? | |
| Jul 7, 2021 at 9:42 | history | edited | asv |
edited tags
|
|
| Jul 7, 2021 at 7:12 | comment | added | markvs | It is true in every CAT(0) space. Must be in Bridson-Haefliger. | |
| Jul 7, 2021 at 6:50 | history | asked | asv | CC BY-SA 4.0 |