Timeline for Convex body with affine-equivalent cross-sections
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Mar 11, 2016 at 18:41 | vote | accept | Sergei Ivanov | ||
| Mar 11, 2016 at 16:59 | comment | added | Deane Yang | You can also see Note 7.2 on page 290 of Richard Gardner's book "Geometric Tomography". This can be viewed on Amazon. | |
| Mar 11, 2016 at 14:43 | comment | added | Fedor Petrov | This sounds interesting, I do not know such results. | |
| Mar 11, 2016 at 14:05 | history | edited | Fedor Petrov | CC BY-SA 3.0 |
added 193 characters in body
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| Mar 11, 2016 at 13:11 | comment | added | Sergei Ivanov | Yes, as well as for the cylinder over any planar convex set. I was thinking about the strictly convex case. I can prove the local version for smooth strictly convex bodies and $k=2$. | |
| Mar 11, 2016 at 12:54 | comment | added | Fedor Petrov | This is definitely false: for cube, there is an open set of sections which are parallelograms, thus equivalent. | |
| Mar 11, 2016 at 12:42 | comment | added | Sergei Ivanov | Thanks! By chance, do you know anything about the local variant: if there is an open set of planes whose sections are equivalent, then these sections are ellipses? | |
| Mar 11, 2016 at 9:52 | history | answered | Fedor Petrov | CC BY-SA 3.0 |