Extremum properties of the new ellipsoid

Authors

  • Yuan Jun
  • Si Lin
  • Leng Gangsong

DOI:

https://doi.org/10.5556/j.tkjm.38.2007.86

Abstract

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) $.

Author Biographies

Yuan Jun

School of Mathematics and Computer Science, Nanjing Normal University, 210097, Nanjing, P.R. China.

Si Lin

College of Science, Beijing Forestry University, Beijing, 100083, P.R. China.

Leng Gangsong

Department of Mathematics, Shanghai University, Shanghai, 200444, P.R. China.

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Published

2007-06-30

How to Cite

Jun, Y., Lin, S., & Gangsong, L. (2007). Extremum properties of the new ellipsoid. Tamkang Journal of Mathematics, 38(2), 159-165. https://doi.org/10.5556/j.tkjm.38.2007.86

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Section

Papers