Journal of Convex Analysis 34 (2027), No. 1, 195--207
Copyright Heldermann Verlag 2027
Barycentric Stability of Nonlocal Perimeters: the Convex Case
Chiara Gambicchia
Scuola Normale Superiore, Pisa, Italy
chiara.gambicchia@sns.it
Enzo Maria Merlino
Dip. di Matematica, Alma Mater Studiorum Università di Bologna, Italy
enzomaria.merlino2@unibo.it
Berardo Ruffini
Dip. di Matematica, Alma Mater Studiorum Università di Bologna, Italy
berardo.ruffini@unibo.it
Matteo Talluri
Dip. di Matematica, Alma Mater Studiorum Università di Bologna, Italy
matteo.talluri@unibo.it
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 B. Fuglede [Lower estimate of the isoperimetric deficit of convex domains in Rn in terms of asymmetry, Geom. Dedicata 47/1 (1993) 41--48]. 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: Fractional perimeter, quantitative isoperimetric inequality, barycentric asymmetry.
MSC: 52A38, 49K40, 52A05; 28A75, 49Q10.
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