Quasi-minimal sets and John domains in dimension 2 and 3

Quasi-minimal surfaces (in the sense of David and Semmes) are sets whose area can be decreased by deformations, but only up to a fixed percentage. This notion allows to represent surfaces minimizing surface energies with possibly highly irregular coefficients. In this talk, I will present a joint work [LT] with Yana Teplitskaya to determine their optimal regularity in dimension 2 and 3.

[LT] : C. Labourie, Y. Teplitskaya. Optimal regularity for quasiminimal sets of codimension one in R2 and R3 (preprint)