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Isoperimetric and Geometric Inequalities in Quantitative Form: Stein’s Method Approach

Year: 2026

Type: article

Abstract: . We adapt Stein’s method to isoperimetric and geometric inequalities. The main challenge is the treatment of boundary terms. We address this by using an elliptic PDE with an oblique boundary condition. We apply our geometric formulation of Stein’s method to obtain stability in the class of nearly spherical sets for the Brock–Weinstock inequality, the isoperimetric inequality under a constraint on Steklov’s first nonzero eigenvalue, and a combination of weighted and unweighted perimeters. All stability results are formulated with respect to the [Formula: see text]-Zolotarev distance, [Formula: see text], that we introduce to interpolate between the Fraenkel asymmetry and the Kantorovich distance.

Source: SIAM Journal on Mathematical Analysis

DOI: 10.1137/25m1741005

Author: Jordan Serres

Institutions: Université Toulouse III - Paul Sabatier, Institut National des Sciences Appliquées de Toulouse, Sorbonne Université, Laboratoire de Probabilités, Statistique et Modélisation, Institut de Mathématiques de Toulouse

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4403970148

FWCI:

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