Hausdorff measure

We introduce methods to cope with self-similar sets when we do not assume any separation condition. For a self-similar set K ⊆ ℝᵈ we establish a similarity dimension-like formula for Hausdorff dimension regardless of any separation condition. By the application of this result we…

The Schramm-Loewner evolutions (SLEs) are a one-parameter family of random curves, introduced by Oded Schramm, which are describing the scaling limit of many critical two-dimensional models arising from statistical physics. So far the existence of scaling limit has been shown fo…