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- W2004809009 abstract "We choose a uniform random point in a given convex body K in n- dimensional Euclidean space and through that point the secant of K with random direction chosen independently and isotropically. Given the volume of K , the expectation of the length of the resulting random secant of K was conjectured by Enns and Ehlers [5] to be maximal if K is a ball. We prove this, and we also treat higher-dimensional sections defined in an analogous way. Next, we consider a finite number of independent isotropic uniform random flats meeting K , and we prove that certain geometric probabilities connected with these again become maximal when K is a ball." @default.
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- W2004809009 date "1985-09-01" @default.
- W2004809009 modified "2023-09-25" @default.
- W2004809009 title "Inequalities for random flats meeting a convex body" @default.
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- W2004809009 doi "https://doi.org/10.1017/s0021900200029466" @default.
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