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arXiv · 2610.35809

Parabolic Rectifiable Reifenberg for Measures

Robert Koirala
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Abstract

We announce a structure theory for measures on $\mathbb{R}^n\times\mathbb{R}$ 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.

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Robert Koirala. 2026-10-26. Parabolic Rectifiable Reifenberg for Measures. https://arxiv.org/abs/2610.35809

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