{"id":"openai-math/Pettys-projection-volume-conjecture-in-dimensions-at-least-four","pdf":"https://github.com/openai/math/blob/main/preprints/Pettys-projection-volume-conjecture-in-dimensions-at-least-four-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Pettys-projection-volume-conjecture-in-dimensions-at-least-four-September-24-2026","tags":["convex-geometry","projection-bodies","geometric-inequalities"],"score":0,"title":"Petty’s projection-volume conjecture in dimensions at least four","domain":"Convex and metric geometry","family":"088","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MG","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":true,"family_title":"Sharp projection-body inequalities and a counterexample to simplex maximization"}