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Parabolic Rectifiable Reifenberg for Measures
Abstract
We announce a structure theory for measures on ℝn×ℝ equipped with the parabolic distance. Our results include a parabolic rectifiable Reifenberg theorem for arbitrary Radon measures, qualitative and quantitative characterizations of regular parabolic rectifiability by Jones square functions, and sharp results for Lp beta numbers. The results hold in every parabolic dimension and extend the theories of Edelen--Naber--Valtorta, Azzam--Tolsa and David--Semmes to space-time. The stated theorems and corollaries, together with their proofs, are formalized in Lean~4 with Mathlib.
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BibTeX
@misc{koirala2026parabolic,
title = {{Parabolic Rectifiable Reifenberg for Measures}},
author = {Robert Koirala},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35809},
eprint = {2610.35809},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35809},
}
RIS
TY - UNPB
TI - Parabolic Rectifiable Reifenberg for Measures
AU - Robert Koirala
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35809
UR - https://arxiv.org/abs/2610.35809
AB - We announce a structure theory for measures on ℝ^n×ℝ equipped with the parabolic distance. Our results include a parabolic rectifiable Reifenberg theorem for arbitrary Radon measures, qualitative and quantitative characterizations of regular parabolic rectifiability by Jones square functions, and sharp results for L^p beta numbers. The results hold in every parabolic dimension and extend the theories of Edelen--Naber--Valtorta, Azzam--Tolsa and David--Semmes to space-time. The stated theorems and corollaries, together with their proofs, are formalized in Lean~4 with Mathlib.
ER -