Fractal Geometry Seminar

Javad Mashreghi, Pure Math Department Visitor from University of Laval

“The capacity of generalized Cantor sets”

The classical Cantor set is defined on the closed unit interval [0,1] and has a very symmetric structure. We provide two general definitions: 1) Cantor set and 2) K-capacity both on an arbitrary compact metric space. No doubt, the classical Cantor set and the logarithmic capacity are under this giant umbrella. Then we effectively estimate the K-capacity of a Cantor set. This result is the key ingredient in studying the one-box condition for Carleson measures of the Dirichlet space.

MC 5403