<p>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 deformation of an element of the sequence to the limit.</p>

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The Space-time connectivity theorem for normal currents

  • Paolo Bonicatto,
  • Filip Rindler,
  • Harry Turnbull

摘要

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 deformation of an element of the sequence to the limit.