Least Wasserstein distance between disjoint shapes with perimeter regularization

Michael Novack, Ihsan Topaloglu, Raghavendra Venkatraman

We prove the existence of global minimizers to the double minimization problem \[ \inf\Big\{ P(E) + λW_p(\mathcal{L}^n \lfloor \, E,\mathcal{L}^n \lfloor\, F) \colon |E \cap F| = 0…