A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is `application/pdf`

.

##
###
Lie Groups That are Closed at Infinity

1989
*
Transactions of the American Mathematical Society
*

A noncompact Riemannian manifold M is said to be closed at infinity if no bounded volume form which is also bounded away from zero can be written as the exterior derivative of a bounded form on M . The isoperimetric constant of M is defined by h(M) = inf{vol(3.S)/ vol^)} where 5 ranges over compact domains with boundary in M . It is shown that a Lie group G with left invariant metric is closed at infinity if and only if h(G) = 0 if and only if G is amenable and unimodular. This result relates

doi:10.2307/2001426
fatcat:gkh7mjilpzha7ihvi3q2kt7ipu