Barycentric stability of nonlocal perimeters: the convex case

2025/06/04 by Chiara Gambicchia, Gambicchia, Chiara, Enzo Maria Merlino +5
Computer Science · Mathematics · #Optimization and Variational Analysis #Contact Mechanics and Variational Inequalities #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2506.03776

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.

Citations

• Quantitative isoperimetric inequalities in capillarity problems and cones in strong and barycentric forms
• The sharp quantitative barycentric isoperimetric inequality for bounded sets
• Hitchhiker's guide to the fractional Sobolev spaces
• Hitchhikerʼs guide to the fractional Sobolev spaces
• A Selection Principle for the Sharp Quantitative Isoperimetric Inequality
• Nonlocal minimal surfaces

Related

• Isoperimetric problems for a nonlocal perimeter of Minkowski type
• Quantitative isoperimetric inequalities in capillarity problems and cones in strong and barycentric forms
• The sharp quantitative barycentric isoperimetric inequality for bounded sets
• A quantitative isoperimetric inequality for fractional perimeters
• Quantitative stability in the isodiametric inequality via the isoperimetric inequality