Geometric formulas demonstrate new nonlocal insights, suggesting a novel approach to classical mathematics.
Inspired by a classical identity proved by James Simons, we establish a new geometric formula in a nonlocal, possibly fractional, setting. Our formula also recovers the classical case in the limit, thus providing an approach to Simons' work that does not heavily rely on differential geometry.
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Dipierro et al. (2025) studied this question.
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