Inequalities for random flats meeting a convex body
1985 ◽
Vol 22
(03)
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pp. 710-716
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Keyword(s):
We choose a uniform random point in a given convex bodyKinn-dimensional Euclidean space and through that point the secant ofKwith random direction chosen independently and isotropically. Given the volume ofK, the expectation of the length of the resulting random secant ofKwas conjectured by Enns and Ehlers [5] to be maximal ifKis 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 meetingK, and we prove that certain geometric probabilities connected with these again become maximal whenKis a ball.
Keyword(s):
The mathematical foundations of anelasticity: existence of smooth global intermediate configurations
2021 ◽
Vol 477
(2245)
◽
pp. 20200462
2009 ◽
Vol 52
(3)
◽
pp. 361-365
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Keyword(s):
2015 ◽
Vol 52
(3)
◽
pp. 386-422
Keyword(s):
1962 ◽
Vol 58
(2)
◽
pp. 217-220
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Keyword(s):
1972 ◽
Vol 14
(3)
◽
pp. 336-351
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2014 ◽
Vol 46
(04)
◽
pp. 919-936
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