Bibliographic Details
| Title: |
On the density problem in the parabolic space |
| Authors: |
Merlo, Andrea, Mourgoglou, Mihalis, Puliatti, Carmelo |
| Publication Year: |
2022 |
| Collection: |
Mathematics |
| Subject Terms: |
Mathematics - Metric Geometry, Mathematics - Classical Analysis and ODEs, 28A75, 28A78, 30L99 |
| More Details: |
In this work we extend many classical results concerning the relationship between densities, tangents and rectifiability to the parabolic spaces, namely $\mathbb{R}^{n+1}$ equipped with parabolic dilations. In particular we prove a Marstrand-Mattila rectifiability criterion for measures of general dimension, we provide a characterisation through densities of intrinsic rectifiable measures, and we study the structure of $1$-codimensional uniform measures. Finally, we apply some of our results to the study of a quantitative version of parabolic rectifiability: we prove that the weak constant density condition for a $1$-codimensional Ahlfors-regular measure implies the bilateral weak geometric lemma. |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2211.04222 |
| Accession Number: |
edsarx.2211.04222 |
| Database: |
arXiv |
