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- W3126256288 abstract "We consider the family of $r$-parallel sets in $mathbb{R}^d$, that is sets of the form $A_r=A+rB_2^n$, where $B_2^n$ is the unit Euclidean ball and $A$ is an arbitrary Borel set. We show that the ratio between the upper surface area measure of an $r$-parallel set and its volume is upper bounded by $d/r$. Equality is achieved for $A$ being a single point. As a consequence of our main result we show that the Gaussian upper surface area measure of an $r$-parallel set is upper bounded by $18d max(sqrt{d},r^{-1})$. Moreover, we observe that there exists a $1$-parallel set with Gaussian surface area measure at least $0.28 cdot d^{1/4}$." @default.
- W3126256288 created "2021-02-15" @default.
- W3126256288 creator A5016569839 @default.
- W3126256288 date "2021-02-06" @default.
- W3126256288 modified "2023-09-27" @default.
- W3126256288 title "Reverse isoperimetric inequalities for parallel sets" @default.
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- W3126256288 hasPublicationYear "2021" @default.
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