The pointed flat compactness theorem for locally integral currents

2010/02/12 by Urs Lang, Stefan Wenger, Lang, Urs +1
Computer Science · Mathematics · #49Q15 #53C23 #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1002.2633

openalex publication_date 2010/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently, a new embedding/compactness theorem for integral currents in a sequence of metric spaces has been established by the second author. We present a version of this result for locally integral currents in a sequence of pointed metric spaces. To this end we introduce another variant of the Ambrosio--Kirchheim theory of currents in metric spaces, including currents with finite mass in bounded sets.

Related

• Plateau's problem for integral currents in locally non-compact metric spaces
• Compactness for manifolds and integral currents with bounded diameter and volume
• Flat convergence for integral currents in metric spaces
• Decomposition of integral metric currents
• The superposition principle for local 1-dimensional currents