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- W1628204572 abstract "Some geometric facts concerning sets with positive reach in the Euclidean $d$-dimensional space ${bf E}^d$ are proved. For $x_1$ and $x_2$ in ${bf E}^d$ and $R>0$ let us denote by ${mathfrak H}(x_1,x_2,R)$ the intersection of all closed balls of radius $R$ containing $x_1$ and $x_2$. For a compact subset $K$ of ${bf E}^d$ we prove that ${rm reach}(K)ge R$ if and only if for every $x_1,x_2in K$ such that $Vert x_1-x_2Vert 0$ and $D$ is a closed ball of radius less than or equal to $R$ (intersecting $K$) then ${rm reach}(Kcap D)ge R$. We also give a necessary and sufficient condition such that $Asubset{bf E}^d$ admits a minimal cover (with respect to inclusion) of ${rm reach}ge R$." @default.
- W1628204572 created "2016-06-24" @default.
- W1628204572 creator A5033641890 @default.
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- W1628204572 date "2007-03-21" @default.
- W1628204572 modified "2023-09-27" @default.
- W1628204572 title "On geometric properties of sets of positive reach in ${bf E}^d$" @default.
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