Optimal regularity for quasiminimal sets of codimension one in \R² and \R³

2024/11/11 by Camille Labourie, Labourie, Camille, Yana Teplitskaya +1 · 1 citation
Computer Science · Mathematics · #49K99 #49Q20 #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2411.07210

openalex publication_date 2024/11/11 · openalex created_date 2024/11/15 · openalex updated_date 2026/07/28

Abstract

Quasiminimal sets are sets for which a pertubation can decrease the area but only in a controlled manner. We prove that in dimensions 2 and 3, such sets separate a locally finite family of local John domains. Reciprocally, we show that this property is a sufficient for quasiminimality. In addition, we show that quasiminimal sets locally separate the space in two components, except at isolated points in \R² or out a of subset of dimension strictly less than N-1 in \R^N.

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