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Intrinsic and dual volume deviations of convex bodies and polytopes | | Florian Besau
; Steven Hoehner
; Gil Kur
; | | Date: |
21 May 2019 | | Abstract: | We establish estimates for the asymptotic best approximation of the Euclidean
unit ball by polytopes under a notion of distance induced by the intrinsic
volumes. We also introduce a notion of distance between convex bodies that is
induced by the Wills functional, and apply it to derive asymptotically sharp
bounds for approximating the ball in high dimensions. Remarkably, it turns out
that there is a polytope which is almost optimal with respect to all intrinsic
volumes simultaneously, up to an absolute constant.
Finally, we establish asymptotic formulas for the best approximation of
smooth convex bodies by polytopes with respect to a distance induced by dual
volumes, which originate from Lutwak’s dual Brunn-Minkowski theory. | | Source: | arXiv, 1905.8862 | | Services: | Forum | Review | PDF | Favorites | |
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