Monday Analysis Seminar: Volume doubling property, quasisymmetry and time changes of Brownian motions

2013-11-18 14:45 - 2013-11-18 16:30
Faculty of Science Buliding #3 Room 210
Jun Kigami (Kyoto University)
We consider time changes of the Brownian motions of the Sierpinski carpets including the Euclidean spaces under measures which are not necessarily self-similar. In short, a time change is to put a (singular) density of a medium and locally change the speed of the Brownian motion. First we give a sufficient condition for time change. Then under the volume doubling property to the normalized Hasudorff measure, we show the existence of a metric which is quasisymmetric to the (restriction of) Euclidean metric and under which we have nice upper and lower heat kernel estimates.