{"id":"openai-math/The-logarithmic-Brunn-Minkowski-conjecture","pdf":"https://github.com/openai/math/blob/main/preprints/The-logarithmic-Brunn-Minkowski-conjecture-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-logarithmic-Brunn-Minkowski-conjecture-September-23-2026","tags":["convex-geometry","brunn-minkowski","log-concave-measures"],"score":0,"title":"The logarithmic Brunn–Minkowski conjecture","domain":"Convex and metric geometry","family":"091","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MG","summary":"We prove the logarithmic Brunn–Minkowski conjecture for arbitrary origin-symmetric convex bodies in every dimension. The theorem also gives the symmetric L p Brunn–Minkowski inequality for every $`0\\lt p\\lt 1`$. Combined with Saroglou's transfer theorem and a support-subspace reduction, it yields the logarithmic inequality for every even log-concave Radon measure and the scalar-dilation $`(B)`$-conjecture.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":1,"published":"2026-09-23","reactions":{},"discussion":[{"url":"https://gilkalai.wordpress.com/2026/10/07/updates-sharing-ai-progress-on-mathematics-amazing-and-my-lecture-plans/#:~:text=a%20proof%20of%20the%20logarithmic%20Brunn%E2%80%93Minkowski%20conjecture%20for%20origin-symmetric%20convex%20bodies%20in%20every%20dimension","date":"2026-10-07","kind":"web","site":"Combinatorics and more","text":"a proof of the logarithmic Brunn–Minkowski conjecture for origin-symmetric convex bodies in every dimension. The two-point Chowla conjecture. In EDP Reflections and Celebrations (2015), I discussed Tao’s logarithmically averaged Chowla and Elliott results and their role in solving the Erdős…","added":"2026-10-24","title":"Updates: Sharing AI progress on mathematics (amazing!); and my lecture plans"}],"formalized":true,"family_title":"Logarithmic and L p Brunn–Minkowski inequalities and the B-conjecture"}