Non-local distance functions and geometric regularity
Classical Analysis and ODEs
2022-08-16 v1
Abstract
We establish the equivalence between the regularity (rectifiability) of sets and suitable estimates on the oscillation of the gradient for smooth non-local distance functions. A prototypical example of such a distance was introduced, as part of a larger PDE theory, by Guy David, Joseph Feneuil, and the third author. The results apply to all dimensions and co-dimensions, require no underlying topological assumptions, and provide a surprisingly rich class of analytic characterizations of rectifiability.
Cite
@article{arxiv.2208.07342,
title = {Non-local distance functions and geometric regularity},
author = {Max Engelstein and Cole Jeznach and Svitlana Mayboroda},
journal= {arXiv preprint arXiv:2208.07342},
year = {2022}
}
Comments
44 pages. Comments welcome