M. Goldman

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math.AP2025

Quantitative estimates for bending energies and applications to non-local variational problems

Michael Goldman, Matteo Novaga, Matthias RÃ¶ger

We discuss a variational model, given by a weighted sum of perimeter, bending and Riesz interaction energies, that could be considered as a toy model for charged elastic drops. The…

math.AP2024

Set-decomposition of normal rectifiable G-chains via an abstract decomposition principle

Michael Goldman, BenoÃ®t Merlet

We introduce the notion of set-decomposition of a normal G-flat chain. We show that any normal rectifiable $G$ -flat chain admits a decomposition in set-indecomposable sub-chains. T…

math.AP2024

Uniform $C^{1, I^\pm}$ -regularity for almost-minimizers of some nonlocal perturbations of the perimeter

Michael Goldman, BenoÃ®t Merlet, Marc Pegon

In this paper, we establish a $C^{1, I^\pm}$ -regularity theorem for almost-minimizers of the functional $F_{ε, I^^{3}} = P - I^^{3} P_{ε}$ , where $I^^{3} \in (0, 1)$ and $P_{\…

Quantitative estimates for bending energies and applications to non-local variational problems

Set-decomposition of normal rectifiable G-chains via an abstract decomposition principle

Uniform C1,I^±-regularity for almost-minimizers of some nonlocal perturbations of the perimeter

Uniform $C^{1, I^\pm}$ -regularity for almost-minimizers of some nonlocal perturbations of the perimeter