Two examples related to conical energies
Classical Analysis and ODEs
2023-06-28 v2 Metric Geometry
Abstract
In a recent article we introduced and studied conical energies. We used them to prove three results: a characterization of rectifiable measures, a characterization of sets with big pieces of Lipschitz graphs, and a sufficient condition for boundedness of nice singular integral operators. In this note we give two examples related to sharpness of these results. One of them is due to Joyce and M\"{o}rters, the other is new and could be of independent interest as an example of a relatively ugly set containing big pieces of Lipschitz graphs.
Cite
@article{arxiv.2011.12717,
title = {Two examples related to conical energies},
author = {Damian Dąbrowski},
journal= {arXiv preprint arXiv:2011.12717},
year = {2023}
}
Comments
23 pages, 2 figures; reformulated Lemma 2.3, other minor improvements, results unchanged; to appear in Ann. Acad. Sci. Fenn. Math