Journal of the Ramanujan Mathematical Society
Volume 31, Issue 3, September 2016 pp. 307–321.
Isoperimetric inequalities using Varopoulos transport
Authors:
Antara Mukherjee
Author institution:Department of Mathematics and Computer Science, The Citadel, Charleston, SC
Summary:
The main results of this paper provide upper bounds of the second
order Dehn functions of three-dimensional groups Nil and Sol.
These upper bounds are obtained by using the Varopoulos transport
argument on dual graphs. The idea is to reduce the original
isoperimetric problem involving volumes of three-dimensional balls
and areas of their boundary spheres to a problem involving
Varopoulos' notion of volume and boundary of finite domains in
dual graphs.
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