Geometry of Locally Compact Groups of Polynomial Growth and Shape of Large Balls
نویسنده
چکیده
We show that any locally compact group G with polynomial growth is weakly commensurable to some simply connected solvable Lie group S, the Lie shadow of G. We then study the shape of large balls and show, generalizing work of P. Pansu, that after a suitable renormalization, they converge to a limiting compact set which can be interpreted geometrically. As a consequence, we get the volume asymptotics of large balls. We discuss the speed of convergence, treat some examples and give an application to ergodic theory. We also answer a question of Burago [5] and recover some results of Stoll [24].
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تاریخ انتشار 2007