Geometry and topology · Oct 6, 2026
Sharp projection-body inequalities and a counterexample to simplex maximization
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.
Contributors
Unreleased OpenAI model
AI systems: Unreleased OpenAI model