Spectral distribution and $L^2$-isoperimetric profile of Laplace operators on groups

Details Spectral distribution and $L^2$-isoperimetric profile of Laplace operators on groups Spectral distribution and $L^2$-isoperimetric profile of Laplace operators on groups

2009-01-02

arxiv.org/abs/0901.0271v3

Mathematics

Group Theory

22 pages; changed title; improved exposition and gave more details in some of the proofs

Scientific paper

We give a formula relating the $L^2$-isoperimetric profile to the spectral distribution of the Laplace operator associated to a finitely generated group $\Gamma$ or a Riemannian manifold with a cocompact, isometric $\Gamma$-action. As a consequence, we can apply techniques from geometric group theory to estimate the spectral distribution of the Laplace operator in terms of the growth and the F{\o}lner's function of the group, generalizing previous estimates by Gromov and Shubin. This leads, in particular, to sharp estimates of the spectral distributions for several classes of solvable groups. Furthermore, we prove the asymptotic invariance of the spectral distribution under changes of measures with finite second moment.

Affiliated with

Also associated with

No associations

Rating

Spectral distribution and $L^2$-isoperimetric profile of Laplace operators on groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Spectral distribution and $L^2$-isoperimetric profile of Laplace operators on groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spectral distribution and $L^2$-isoperimetric profile of Laplace operators on groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-381197