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arXiv · 2510.08360

The Space-Time Connectivity Theorem for Normal Currents

Paolo Bonicatto·Filip Rindler·Harry Turnbull
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Abstract

This work establishes a Space-Time Connectivity Theorem for normal currents. In analogy with classical results of Federer and Fleming, 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 to 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.

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Paolo Bonicatto, Filip Rindler, Harry Turnbull. 2025-10-09. The Space-Time Connectivity Theorem for Normal Currents. https://arxiv.org/abs/2510.08360

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