Timeline for A question on the theorem of Minkowski-Hlawka
Current License: CC BY-SA 3.0
7 events
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| Mar 13, 2016 at 16:20 | history | edited | user9072 |
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| May 17, 2013 at 7:17 | comment | added | alvarezpaiva | @Yoav: Thanks for your input. I don't see why the min should be achieved either and I'm starting to suspect it is not. What puzzles me is that no one seems to mention this. | |
| May 16, 2013 at 22:16 | comment | added | Yoav Kallus | I guess T doesn't have to be bisectible into two convex regions, but, still, I don't see a good reason why the minimum should be achieved. | |
| May 16, 2013 at 21:08 | comment | added | Yoav Kallus | Looking again at Sergei's answer to the other question, it seems like what you're asking for here should fail: let T=S∪(−S), then among all S′ such that T=S′∪(−S') (and therefore Δ(S)=Δ(S′)) we minimize the volume by letting S′ be the intersection of T with a half-space through the origin. Since this minimum is never achieved so long as the origin is in the interior, the minimum of vol(S)/Δ(S) is never achieved. Am I missing something? | |
| May 16, 2013 at 20:50 | comment | added | Yoav Kallus | Also worth noting, the even easier case: the minimum of $S\mapsto\operatorname{vol}(S)/\Delta(S-S)$ is actually known among two-dimensional convex bodies (the triangle). | |
| May 16, 2013 at 20:35 | comment | added | Yoav Kallus | related: mathoverflow.net/questions/125531/… | |
| May 16, 2013 at 19:53 | history | asked | alvarezpaiva | CC BY-SA 3.0 |