{"id":"openai-math/Riesz-transforms-and-uniform-rectifiability-in-higher-codimension","pdf":"https://github.com/openai/math/blob/main/preprints/Riesz-transforms-and-uniform-rectifiability-in-higher-codimension-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Riesz-transforms-and-uniform-rectifiability-in-higher-codimension-September-24-2026","tags":["harmonic-analysis","geometric-measure-theory","rectifiability"],"score":0,"title":"Riesz transforms and uniform rectifiability in higher codimension","domain":"Real and complex analysis","family":"081","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CA","summary":"We prove that an n -Ahlfors–David regular Radon measure on ℝ d is uniformly n -rectifiable if its n -dimensional Riesz transform is uniformly bounded from scalar $`L^2(\\mu)`$ to vector-valued $`L^2(\\mu)`$ over all positive hard truncations, for integers d ≥ 4 and $`2\\le n\\le d-2`$. This gives a positive answer to the David–Semmes Riesz-transform question in its remaining higher-codimension range. The conclusion gives uniform big pieces of Lipschitz images of Euclidean balls.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":true,"family_title":"Riesz transforms and rectifiability in higher codimension"}