University of Washington, Seattle

Two dimensional minimal cones were fully classified by Jean Taylor in the mid

70's.  In joint work with G. David and T. De Pauw we prove that a closed

set which is close to a minimal cone at all scales and at all locations is

locally a bi-Hoelder image of a minimal cone.  This result is analogous to

Reifenberg's disk theorem.  A couple of applications will be discussed.