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A nonlocal approximation of the area in codimension two

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arxiv 2406.13696 v2 pith:D6X7N42S submitted 2024-06-19 math.DG math.APmath.OC

Michele Caselli , Mattia Freguglia , Nicola Picenni This is my paper · ORCID
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keywords areaconvergencedimensionalapproximationclosedcodimensionflatfractional
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abstract

For $s\in (0,1)$ we introduce a notion of fractional $s$-mass on $(n-2)$-dimensional closed, orientable surfaces in $\R^n$. Moreover, we prove its $\Gamma$-convergence, with respect to the flat topology, and pointwise convergence to the $(n-2)$-dimensional area.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Harmonic maps to the circle with higher dimensional singular set

    math.DG 2024-11 conditional novelty 8.0 of 10

    Singular S1-valued harmonic maps with prescribed codimension-2 singular set exist on closed manifolds, and three variational relaxations share the same renormalised interaction energy.

  2. $\Gamma$-convergence of the $p$-Dirichlet energy for manifold-valued maps

    math.AP 2025-05 accept novelty 7.0 of 10

    As p approaches k from below, the rescaled p-Dirichlet energies of maps into a manifold Gamma-converge to the mass of the n-dimensional flat chain that solves the homological Plateau problem for the boundary datum.

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