The Space-Time Connectivity Theorem for Normal Currents

2025/10/09 by Paolo Bonicatto, Bonicatto, Paolo, Filip Rindler +3
#49Q15 #53C65 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2510.08360

Abstract

This work establishes a Space-Time Connectivity Theorem for normal currents. In analogy to classical results by Federer and Fleming as well as a recent theorem for integral currents by the second author, this result allows one to witness the weak* convergence of a uniformly bounded sequence of boundaryless normal currents with a space-time normal current that connects the elements of the sequence with their limit. The space-time setting is distinguished from the classical case in that this connecting current has a time coordinate and thus constitutes a progressive-in-time way to deform an element of the sequence to the limit.

Citations

• Homogenization of elasto-plastic evolutions driven by the flow of dislocations
• Energetic solutions to rate-independent large-strain elasto-plastic evolutions driven by discrete dislocation flow
• Space-time integral currents of bounded variation
• Space-time integral currents of bounded variation
• Linear isoperimetric inequality for normal and integral currents in compact subanalytic sets
• On the differentiability of Lipschitz functions with respect to measures\n in the Euclidean space
• Partial regularity and smooth topology-preserving approximations of\n rough domains
• Partial regularity and smooth topology-preserving approximations of rough domains
• Normal and Integral Currents

Related

• Unrectifiable normal currents in Euclidean spaces
• The superposition principle for local 1-dimensional currents
• Examples of 2-unrectifiable normal currents
• Space-time integral currents of bounded variation
• Structure of Metric 1-currents: approximation by normal currents and representation results