Parabolic rectifiability, tangent planes and tangent measures

Abstract

We define rectifiability in ${\mathbb{R}}^n\times \mathbb{R}$ with a parabolic metric in terms of $C^1$ 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.

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