OpenAI research collection · 2 manuscripts · Source checked 2026-10-19
Proves Petty's projection-volume conjecture in the remaining dimensions n ≥ 4: ellipsoids uniquely minimize projection-body volume at fixed body volume. Also establishes the full Lutwak–Petty projection inequalities. In contrast, products of simplices exceed Brannen's proposed simplex maximum for normalized projection-body volume by an exponential factor in every sufficiently large dimension.
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We prove that ellipsoids uniquely minimize the volume of the projection body among convex bodies of fixed volume in every dimension at least four. This proves Petty's projection-volume conjecture in these dimensions.
This PDF is listed in OpenAI's formalization catalogue. See the scope and dependencies before interpreting coverage.
The product of two ten-dimensional simplices has larger normalized projection-body volume than a twenty-dimensional simplex. This gives a counterexample to Brannen's proposed simplex maximum.
This PDF is listed in OpenAI's formalization catalogue. See the scope and dependencies before interpreting coverage.
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