Timeline for More refined versions of Brunn–Minkowski inequality and/or Prékopa–Leindler inequality
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Oct 9, 2016 at 14:48 | comment | added | Paata Ivanishvili | What about Brunn-Minkowski inequality but with essential minkowski sum? In this case $A+_{e}B=\{z \in \mathbb{R}^{n} : \mu(A \cap (\{z\}-B))\neq 0\}$. Clearly if $A$ or $B$ has $n$ dimensional Lebesgue measure zero then always $\mu(A \cap (\{z\}-B))=0$, and aessential minkowsi sum does not give you anything. So then we have just equality $| A+_{e}B|^{1/n}\geq |A|^{1/n}+|B|^{1/n}$ instead of inequality. The same thing with Prekopa--Leindler but with essential supremum. (see the last section en.wikipedia.org/wiki/Minkowski_addition) | |
| Oct 9, 2016 at 6:16 | answer | added | Ivan Izmestiev | timeline score: 1 | |
| Oct 9, 2016 at 5:10 | answer | added | T. Amdeberhan | timeline score: 0 | |
| Oct 9, 2016 at 4:36 | history | asked | SorcererofDM | CC BY-SA 3.0 |