Timeline for gaussian isoperimetric result for minimal measure under translation
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 2, 2018 at 2:13 | vote | accept | Jeremy | ||
| Nov 2, 2018 at 2:13 | answer | added | Jeremy | timeline score: 0 | |
| Oct 30, 2018 at 20:05 | comment | added | Mateusz Kwaśnicki | In general, the set $A$ that minimizes $\int_A f$ given $\int_A g = p$ is the set $A_p = \{f / g < c(p)\}$ for an appropriate $c(p)$. To see this, simply write $$\begin{aligned}\int_A f - \int_{A_p} f &= \int_{A\setminus A_p} f - \int_{A_p\setminus A}f \\&\ge c(p)\int_{A\setminus A_p} g - c(p) \int_{A_p\setminus A}g \\&= c(p)\int_A g - c(p)\int_{A_p} g \\&= c(p) \times p - c(p) \times p = 0.\end{aligned}$$ | |
| Oct 30, 2018 at 19:27 | history | edited | Jeremy | CC BY-SA 4.0 |
deleted 3 characters in body
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| Oct 30, 2018 at 18:18 | history | asked | Jeremy | CC BY-SA 4.0 |