Optimal regularity for quasiminimal sets of codimension one in ${\mathbb{R}}^2$ and ${\mathbb{R}}^3$

Camille Labourie, Yana Teplitskaya

Quasiminimal sets are sets for which a pertubation can decrease the area but only in a controlled manner. We prove that in dimensions $2$ and $3$, such sets separate a locally fini…