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Nov 24, 2013 at 17:23 comment added Sasho Nikolov I know this is a very old question, but let me just say that $E^+$ is the polar body of $E^-$ of $K^\circ$ (the polar body of $K$).
Jan 22, 2012 at 14:26 comment added Mark Meckes Joseph: You didn't indicate whether you are also interested in sharper results which hold under stronger hypotheses on $K$. If so, there are relevant results in the literature on Banach-Mazur distance.
Jan 22, 2012 at 13:25 vote accept Joseph O'Rourke
Jan 22, 2012 at 1:30 comment added Joseph O'Rourke @Bill: Thanks, an insightful remark!
Jan 21, 2012 at 23:24 comment added Bill Johnson All the positive results on Q.2.b that I know are derived from the fact that the ellipsoids are invariant under symmetries of $E$.
Jan 21, 2012 at 21:59 answer added Mark Meckes timeline score: 10
Jan 21, 2012 at 21:35 history asked Joseph O'Rourke CC BY-SA 3.0