An Isoperimetric Inequality for the Heisenberg Groups
نویسنده
چکیده
We show that the Heisenberg groups H 2n+1 of dimension ve and higher, considered as Rieman-nian manifolds, satisfy a quadratic isoperimetric inequality. (This means that each loop of length L bounds a disk of area L 2). This implies several important results about isoperimetric inequalities for discrete groups that act either on H 2n+1 or on complex hyperbolic space, and provides interesting examples in geometric group theory. The proof consists of explicit construction of a disk spanning each loop in H 2n+1 .
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