We consider surfaces which minimize a nonlocal perimeter functional and
we discuss their interior regularity and rigidity properties, in a
quantitative and qualitative way, and their (perhaps rather surprising)
boundary behavior. We present at least a sketch of the proofs of these
results, in a way that aims to be as elementary and self contained as
possible, referring to the papers [CRS10, SV13, CV13, BFV14,FV,DSV15,CSV16]
for full details.
