Another look at a notion of fractional mass in codimension two

Michele Caselli; Mattia Freguglia; Nicola Picenni

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arXiv · 2607.00810

Another look at a notion of fractional mass in codimension two

Michele Caselli·Mattia Freguglia·Nicola Picenni

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Abstract

We study a notion of fractional $s$-mass for codimension-two currents on closed Riemannian manifolds, defined via energy minimization with a prescribed Jacobian constraint. We prove equi-coercivity and $\Gamma$-convergence, with respect to the flat topology, of the $s$-mass on general codimension-two currents. We also prove several additional results for fixed $s$. We establish improved regularity for $s$-harmonic maps that are minimizing among competitors with vanishing Jacobian and show that their singular set has Minkowski dimension at most $n-3$. Moreover, we show that the $s$-mass defined via weak linking, as recently introduced by the authors, agrees with the prescribed Jacobian formulation used here, clarifying the extent to which the $s$-mass depends, or ultimately does not depend, on the way singularities are prescribed.

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Michele Caselli, Mattia Freguglia, Nicola Picenni. 2026-07-01. Another look at a notion of fractional mass in codimension two. https://arxiv.org/abs/2607.00810

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