Timeline for Convex bodies with constant maximal section function in odd dimensions
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 4, 2012 at 2:00 | answer | added | fedja | timeline score: 4 | |
| Jul 15, 2011 at 3:29 | comment | added | fedja | Not really :(. The bodies of constant width (=constant maximal 1-dimensional sections) are not hard to construct because basically you just have to relate pairs of points. When you raise the section dimension, you have to deal with integral transforms. I suspect that this simple R^4 construction went unnoticed because the customary way is to represent convex bodies by their radial or support functions even for the bodies of revolution and the equimeasurability condition is a total mess in such terms. So, it seems like we need a fresh look with some little twist... | |
| Jul 15, 2011 at 3:01 | comment | added | user6976 | Can this help (Meissner bodies): en.wikipedia.org/wiki/Meissner%27s_tetrahedron#Meissner_bodies ? | |
| Jul 15, 2011 at 2:46 | comment | added | Will Jagy | That's right. I knew about curves of constant width, I did not connect that properly with your question. | |
| Jul 15, 2011 at 2:43 | comment | added | user6976 | en.wikipedia.org/wiki/Curve_of_constant_width | |
| Jul 15, 2011 at 2:42 | comment | added | fedja | Planar domains of constant width have been well-known for a long time (normally one thinks of them as having constant projections but all their projections are realized as sections as well). | |
| Jul 15, 2011 at 2:14 | comment | added | Will Jagy | what about $n=2$? | |
| Jul 15, 2011 at 2:08 | history | asked | fedja | CC BY-SA 3.0 |