OpenAI reports Petty’s projection-volume inequality in dimensions at least four
- Mathematics
For every convex body K in Rⁿ with n≥4, its normalized projection-body volume is at least the ellipsoid value, with equality exactly for ellipsoids.
OpenAI reports Petty’s projection-volume inequality in dimensions at least four
- Mathematics
For every convex body K in Rⁿ with n≥4, its normalized projection-body volume is at least the ellipsoid value, with equality exactly for ellipsoids.
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Read the background
For every convex body K in Rⁿ with n≥4, its normalized projection-body volume is at least the ellipsoid value, with equality exactly for ellipsoids.
Why it matters
If correct, completes the higher-dimensional part of Petty’s projection-volume conjecture.
What counts as progress
Do ellipsoids minimize normalized projection-body volume in every dimension at least four?
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OpenAI reports Petty’s projection-volume inequality in dimensions at least four