On the boundary of almost isoperimetric domains

2017/03/07 by Erwann Aubry, Aubry, Erwann, Jean-François Grosjean +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.1703.02587

openalex publication_date 2017/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that finite perimeter subsets of \ℝⁿ⁺¹ with small\nisoperimetric deficit have boundary Hausdorff-close to a sphere up to a subset\nof small measure. We also refine this closeness under some additional a priori\nintegral curvature bounds. As an application, we answer a question raised by B.\nColbois concerning the almost extremal hypersurfaces for Chavel's inequality.\n

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