Timeline for Sharp constant for inequality with convex functions
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Nov 25, 2017 at 21:09 | comment | added | Yaakov Baruch | After thinking a bit more, I think that for affine $f$ a plausible bound may be $\alpha\ge \frac{1}{n+1}|P|$, which seems to be achieved when the kernel of $f$ cuts a hypercube half way between 2 opposite vertices. | |
| Nov 25, 2017 at 1:00 | comment | added | Steve | @Yaakov Baruch I added some examples that might answer your question | |
| Nov 25, 2017 at 0:59 | history | edited | Steve | CC BY-SA 3.0 |
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| Nov 24, 2017 at 20:12 | comment | added | Paata Ivanishvili | I think you are right (at least this is true in dimension n=1 based on my early morning calculations). | |
| Nov 24, 2017 at 13:43 | comment | added | Yaakov Baruch | Just to get some feeling for this question: would it be true that if $f$ is the restriction of an affine map, then a lower bound would be $\alpha\ge 2^{-1}|P|$ (regardless of of $n$)? If so, would that be sharp (for every $P$)? | |
| Nov 21, 2017 at 12:52 | history | edited | Steve | CC BY-SA 3.0 |
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| Nov 21, 2017 at 12:04 | history | asked | Steve | CC BY-SA 3.0 |