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Riesz Transform Bounds Imply Parabolic Uniform Rectifiability of Graphs
Abstract
We prove that if a (k+2)-Ahlfors--David regular measure μ in parabolic space ℙn has support equal to a parabolic Lipschitz graph with sufficiently small Lipschitz constant, and the parabolic Riesz transform is bounded on L2(μ), then μ is parabolic uniformly rectifiable and the graph is regular parabolic Lipschitz. The result holds for every integer 0≤ k≤ n−1.
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BibTeX
@misc{hoffman2026riesz,
title = {{Riesz Transform Bounds Imply Parabolic Uniform Rectifiability of Graphs}},
author = {John Hoffman},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32534},
eprint = {2610.32534},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32534},
}
RIS
TY - UNPB
TI - Riesz Transform Bounds Imply Parabolic Uniform Rectifiability of Graphs
AU - John Hoffman
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32534
UR - https://arxiv.org/abs/2610.32534
AB - We prove that if a (k+2)-Ahlfors--David regular measure μ in parabolic space 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≤ k≤ n−1.
ER -