Published Paper

Inserted: 5 jun 2025
Last Updated: 19 oct 2026

Journal: J. Convex Anal.
Volume: 34
Number: 1
Pages: 144-153
Year: 2027
Doi: https://doi.org/10.68381/jca34011

Abstract:

In this work, we establish a sharp form of a nonlocal quantitative isoperimetric inequality involving the barycentric asymmetry for convex sets. This result can be seen as the nonlocal analogue of the one obtained by Fuglede in 1993. A main tool in the proof is an estimate from below of the fractional perimeter by a negative power of the inradius for convex sets.

Keywords: quantitative isoperimetric inequality, fractional perimeter, Barycentric asymmetry

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