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math.AP2025
A general Frobenius' Theorem via the Transport of Currents
Paolo Bonicatto
A classical result in Differential Geometry states that the flows of two smooth vector fields commute if and only if their Lie Bracket vanishes. In this work, we extend this result…
math.AP2025
The Space-Time Connectivity Theorem for Normal Currents
Paolo Bonicatto, Filip Rindler, Harry Turnbull
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* c…
math.AP2025
Well-posedness of the transport of normal currents by time-dependent vector fields
Paolo Bonicatto, Giacomo Del Nin
We prove existence and uniqueness for the transport equation for currents (Geometric Transport Equation) when the driving vector field is time-dependent, Lipschitz in space and mer…