English

Parabolic rectifiability, tangent planes and tangent measures

Classical Analysis and ODEs 2021-10-11 v4 Metric Geometry

Abstract

We define rectifiability in Rn×R\mathbb{R}^{n}\times\mathbb{R} with a parabolic metric in terms of C1C^1 graphs and Lipschitz graphs with small Lipschitz constants and we characterize it in terms of approximate tangent planes and tangent measures. We also discuss relations between the parabolic rectifiability and other notions of rectifiability.

Keywords

Cite

@article{arxiv.2103.16401,
  title  = {Parabolic rectifiability, tangent planes and tangent measures},
  author = {Pertti Mattila},
  journal= {arXiv preprint arXiv:2103.16401},
  year   = {2021}
}

Comments

32 pages. Many changes to the original version of which the most important are the additions of (1) in Theorem 1.1, Sections 5 and 6, and Example 8.2. new version: 33 pages, Lemmas 2.3, 2.4 and Theorem 4.9 changed, plus several small changes

R2 v1 2026-06-24T00:41:43.608Z