Timeline for Example of non-closed convex hull in a CAT(0) space
Current License: CC BY-SA 4.0
15 events
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| Apr 2, 2021 at 18:52 | history | edited | Anton Petrunin | CC BY-SA 4.0 |
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| Dec 14, 2013 at 20:18 | comment | added | Sergei Ivanov | Thanks, now I understand. Indeed the Euclidean intuition fails. | |
| Dec 14, 2013 at 2:48 | comment | added | Anton Petrunin | @SergeiIvanov, I extended the hint; now it is called "semisolution". I hope it helps. | |
| Dec 14, 2013 at 2:47 | history | edited | Anton Petrunin | CC BY-SA 3.0 |
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| Dec 13, 2013 at 17:49 | comment | added | Sergei Ivanov | @Anton, I don't get it. In any manifold, take a point $p$ and a nearby small ball $B$, and connect $p$ to all points of $B$ by geodesic segments. I believe the resulting set is convex if everything is small enough, yet the conical part of the boundary is filled by geodesics. | |
| Dec 12, 2009 at 18:58 | history | edited | Anton Petrunin | CC BY-SA 2.5 |
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| Dec 12, 2009 at 17:14 | history | edited | Anton Petrunin | CC BY-SA 2.5 |
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| Dec 12, 2009 at 6:34 | comment | added | Suresh Venkat | this is very helpful. However, there are some things that I'm not entirely clear about. * I'm not sure why in your statement about generic 3D manifolds, the geodesic has to be in the ambient space ? * I don't see why this implies the result (I'm not doubting: merely not following) | |
| Dec 12, 2009 at 6:32 | vote | accept | Suresh Venkat | ||
| Dec 11, 2009 at 17:16 | history | edited | Anton Petrunin | CC BY-SA 2.5 |
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| Dec 11, 2009 at 5:39 | history | edited | Anton Petrunin | CC BY-SA 2.5 |
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| Dec 11, 2009 at 5:34 | history | edited | Anton Petrunin | CC BY-SA 2.5 |
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| Dec 11, 2009 at 0:58 | history | edited | Anton Petrunin | CC BY-SA 2.5 |
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| Dec 11, 2009 at 0:44 | history | edited | Anton Petrunin | CC BY-SA 2.5 |
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| Dec 11, 2009 at 0:37 | history | answered | Anton Petrunin | CC BY-SA 2.5 |