月曜解析セミナー： Volume doubling 条件の元でのブラウン運動の時間変更と距離の擬対称変換

2013年 　 11月 18日 14時 45分 ～ 2013年 　 11月 18日 16時 30分

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.