Regularity of sets with quasiminimal boundary surfaces in metric spaces

2011/05/16 by Juha Kinnunen, Kinnunen, Juha, Riikka Korte +5 · 3 citations
Computer Science · Mathematics · #26A45 #28A12 #49Q20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · doi:10.48550/arxiv.1105.3058

openalex publication_date 2011/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper studies regularity of perimiter quasiminimizing sets in metric measure spaces with a doubling measure and a Poincare inequality. The main result shows that the measure theoretic boundary of a quasiminimizing set coincides with the topological boundary. We also show that such a set has finite Minkowski content and apply the regularity theory to study rectifiability issues related to quasiminimal sets in strong A_∞-weighted Euclidean case.

Citations

• Modulus and the Poincar� inequality on metric measure spaces
• Quasiconformal maps in metric spaces with controlled geometry

Cited by

• A strong quantitative form of the fractional isoperimetric inequality
• Spectral comparison and splitting theorems for the infinity-Bakry-Emery Ricci curvature
• Quantitative isoperimetric inequalities in capillarity problems and cones in strong and barycentric forms

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