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arXiv · 2610.32534

Riesz Transform Bounds Imply Parabolic Uniform Rectifiability of Graphs

John Hoffman
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Abstract

We prove that if a $(k+2)$-Ahlfors--David regular measure $μ$ in parabolic space $\mathbb P^n$ has support equal to a parabolic Lipschitz graph with sufficiently small Lipschitz constant, and the parabolic Riesz transform is bounded on $L^2(μ)$, then $μ$ is parabolic uniformly rectifiable and the graph is regular parabolic Lipschitz. The result holds for every integer $0\leq k\leq n-1$.

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John Hoffman. 2026-10-23. Riesz Transform Bounds Imply Parabolic Uniform Rectifiability of Graphs. https://arxiv.org/abs/2610.32534

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