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February 8, 20260 citations

Some nonlocal formulas inspired by an identity of James Simons

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SDS. (Serena) DipierroJTJ. (Jack) ThompsonEVE. (Enrico) Valdinoci

Key Points

  • The aim is to develop a nonlocal geometric formula based on a classical identity by James Simons.
  • Established a new geometric formula in a nonlocal setting.
  • Explored connections to fractional settings.
  • Demonstrated recovery of the classical case in the limit.
  • Presented a new nonlocal geometric formula.
  • Showed the formula aligns with the classical identity under specific conditions.
  • Provided a novel approach to understanding differential geometry.

Abstract

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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Cite This Study

Dipierro et al. (2025) studied this question.

synapsesocial.com/papers/698828850fc35cd7a88480a9https://doi.org/10.17879/11958511860
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