Advertisement

Geometric & Functional Analysis GAFA

, Volume 8, Issue 2, pp 219–233 | Cite as

An isoperimetric inequality for the Heisenberg groups

  • D. Allcock

Abstract.

We show that the Heisenberg groups \( \cal {H}^{2n+1} \) of dimension five and higher, considered as Riemannian 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 \( \cal {H}^{2n+1} \) 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 \( \cal {H}^{2n+1} \).

Keywords

Riemannian Manifold Group Theory Hyperbolic Space Heisenberg Group Discrete Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Verlag, Basel 1998

Authors and Affiliations

  • D. Allcock
    • 1
  1. 1.Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA, e-mail: allcock@math.utah.eduUS

Personalised recommendations