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Two examples related to conical energies

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 …

Sufficient condition for rectifiability involving Wasserstein distance W2

A Radon measure μ is n-rectifiable if it is absolutely continuous with respect to Hn and μ-almost all of suppμ can be covered by Lipschitz images of Rn. In this paper we give two sufficient conditions for …

Necessary condition for rectifiability involving Wasserstein distance W2

A Radon measure μ is n-rectifiable if it is absolutely continuous with respect to n-dimensional Hausdorff measure and μ-almost all of suppμ can be covered by Lipschitz images of Rn⁠. In this paper, we give a necessary …

Characterization of Sobolev-Slobodeckij spaces using curvature energies

We give a new characterization of Sobolev-Slobodeckij spaces W1+s,p(Ω) for pn and $\frac{n}{p}