On the Extreme Points of the Unit Ball in the Space of Solenoidal Vector Measures on the Plane - on, We consider the space of finite divergence-free Borel vector measures; Bonicatto., endowed with the total variation norm. For we present a characterization of the extreme points of the unit ball in this space. This allows one to decompose (for ) any finite divergence-free vector measure into measures induced by closed Lipschitz curves. The results are based on a joint work with P. (Discontinuity, Nonlinearity, and Complexity, 2026)
We consider the space of finite divergence-free Borel vector measures on R^d, endowed with the total variation norm. For d=2 we present a characterization of the extreme points of the unit ball in this space. This allows one to decompose (for d=2) any finite divergence-free vector measure into measures induced by closed Lipschitz curves. The results are based on a joint work with P. Bonicatto.