Extremum properties of the new ellipsoid
2007 ◽
Vol 38
(2)
◽
pp. 159-165
◽
For a convex body $ K $ in $ {\mathbb R}^{n} $, Lutwak, Yang and Zhang defined a new ellipsoid $ \Gamma_{-2}K $, which is the dual analog of the Legendre ellipsoid. In this paper, we prove the following two results: (i) For any origin-symmetric convex body $ K $, there exist an ellipsoid $ E $ and a parallelotope $ P $ such that $ \Gamma_{-2}E \supseteq \Gamma_{-2}K \supseteq \Gamma_{-2}P $ and $ V(E)=V(K)=V(P) $; (ii) For any convex body $K$ whose John point is at the origin, then there exists a simplex $T$ such that $ \Gamma_{-2}K \supseteq \Gamma_{-2}T $ and $ V(K)=V(T) $.
1975 ◽
Vol 77
(3)
◽
pp. 529-546
◽
1972 ◽
Vol 14
(3)
◽
pp. 336-351
◽
2006 ◽
Vol 49
(2)
◽
pp. 185-195
◽
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