Applications of convex geometry to Minkowski sums of m ellipsoids in ℝN: Closed-form parametric equations and volume bounds
Keyword(s):
General results on convex bodies are reviewed and used to derive an exact closed-form parametric formula for the Minkowski sum boundary of [Formula: see text] arbitrary ellipsoids in [Formula: see text]-dimensional Euclidean space. Expressions for the principal curvatures of these Minkowski sums are also derived. These results are then used to obtain upper and lower volume bounds for the Minkowski sum of ellipsoids in terms of their defining matrices; the lower bounds are sharper than the Brunn–Minkowski inequality. A reverse isoperimetric inequality for convex bodies is also given.
2009 ◽
Vol 52
(3)
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pp. 361-365
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2018 ◽
Vol 55
(4)
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pp. 1060-1077
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1953 ◽
Vol 49
(1)
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pp. 54-58
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2017 ◽
Vol 2019
(16)
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pp. 4950-4965
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1970 ◽
Vol 11
(4)
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pp. 385-394
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1995 ◽
Vol 05
(04)
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pp. 413-432
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