"On Dimension of Equilibrium Measures
on Small Sets





Alexander Goncharov

(Bilkent University)



Abstract: There are two natural measures on the classical Cantor set : the Cantor-Lebesgue measure (that is the Hausdorff measure with dimension log 2 / log 3), and the equilibrium measure that minimizes the logarithmic energy. Makarov and Volberg proved in 1986 that these measures are mutually singular. Some generalizations were obtained later  for multidimensional fractals and for Cantor repellers. We discuss the possibility to construct Cantor-type sets for which these measures  coincide or, at least,  are not mutually singular.






Tea and cookies will be served before the seminar.



Date:  Wednesday, February 13, 2012

Time: 14.30

Place: Mathematics Seminar Room, SA-141