Geodesic
Two examples related to conical energies
Damian Dąbrowski1
1Universitat Autònoma de Barcelona, Departament de Matemàtiques and Barcelona Graduate School of Mathematics (BGSMath); and University of Jyväskylä, Department of Mathematics and Statistics
Annales Fennici Mathematici, Tome 47 (2022) no. 1, pp. 261-281

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In a recent article (2021) 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 Mörters (2000), the other is new and could be of independent interest as an example of a relatively ugly set containing big pieces of Lipschitz graphs.
DOI : 10.54330/afm.113378
Keywords: Cone, conical density, quantitative rectifiability, big pieces of Lipschitz graphs, singular integral operators

Damian Dąbrowski  1

1 Universitat Autònoma de Barcelona, Departament de Matemàtiques and Barcelona Graduate School of Mathematics (BGSMath); and University of Jyväskylä, Department of Mathematics and Statistics 
Damian Dąbrowski. Two examples related to conical energies. Annales Fennici Mathematici, Tome 47 (2022) no. 1, pp. 261-281. doi: 10.54330/afm.113378
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