Proves equi-coercivity and Γ-convergence of the s-mass for codim-2 currents and shows equivalence between prescribed-Jacobian and weak-linking formulations, with singular-set dimension bounds for minimizers.
First variation of the fractional $k$-dimensional measure: extending the concept of nonlocal curvature to submanifolds
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abstract
The fractional $k$-dimensional measure of a submanifold of $\mathbb{R}^n$ is a generalization of the fractional perimeter and fractional length appearing in the literature and depends on a parameter $\sigma$ between $0$ and $1$. Here its first variation is computed. The resulting formula is used to define a nonlocal version of the mean-curvature vector for embedded submanifolds. It is shown that in the case where $k=n-1$, this agrees with the nonlocal mean-curvature that has been widely studied.
fields
math.DG 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Another look at a notion of fractional mass in codimension two
Proves equi-coercivity and Γ-convergence of the s-mass for codim-2 currents and shows equivalence between prescribed-Jacobian and weak-linking formulations, with singular-set dimension bounds for minimizers.