Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 081-01. Riesz transforms and uniform rectifiability in higher codimension
Manuscript map · lines 4055–4064
OpenAI@2026-10-07#rem:oai-p-081-01
Authors: OpenAI. Family 081.
Title: Riesz transforms and uniform rectifiability in higher codimension.
Abstract: We prove that an n-Ahlfors–David regular Radon measure on ℝd 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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