{"id":"openai-math/Brennans-conjecture-and-sharp-inverse-square-integral-means","pdf":"https://github.com/openai/math/blob/main/preprints/Brennans-conjecture-and-sharp-inverse-square-integral-means-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Brennans-conjecture-and-sharp-inverse-square-integral-means-September-24-2026","tags":["complex-analysis","conformal-mapping","brennans-conjecture"],"score":0,"title":"Brennan's conjecture and sharp inverse-square integral means","domain":"Real and complex analysis","family":"072","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CA","summary":"We prove Brennan's conjecture: if a simply connected plane domain admits a conformal bijection φ onto the unit disk, then $`|\\varphi'|^s`$ is area-integrable for every $`4/3\\lt s\\lt 4`$. We also prove the sharp inverse-square integral-means exponent $`B_{\\mathcal S}(-2)=1`$ for the normalized schlicht class $`\\mathcal S`$.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":1,"published":"2026-09-24","reactions":{},"discussion":[{"url":"https://arxiv.org/abs/2610.23853","date":"2026-10-16","kind":"web","site":"arXiv.org","text":"In October 2026, OpenAI released two preprints \\cite{openai-brennan,openai-kraetzer}, establishing Brennan's celebrated conjecture~\\cite{brennan,brennan2} and disproving Kraetzer's more general $t^2/4$ conjecture \\cite{kraetzer, kraetzer-thesis}. While validating these results, we observed that…","added":"2026-10-24","title":"Brennan's Conjecture and the Universal Integral Means Spectrum","author":"Ilia Binder, Oleg Ivrii, Istvan Prause, Stanislav Smirnov","record":"arxiv/2610.23853"}],"formalized":true,"family_title":"Brennan's conjecture and the integral-means spectrum"}