Journal of the Ramanujan Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

Isoperimetric Inequalities Using Varopoulos Transport


Affiliations
1 Department of Mathematics and Computer Science, The Citadel, Charleston, SC, United States
     

   Subscribe/Renew Journal


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.
User
Subscription Login to verify subscription
Notifications
Font Size

Abstract Views: 256

PDF Views: 0




  • Isoperimetric Inequalities Using Varopoulos Transport

Abstract Views: 256  |  PDF Views: 0

Authors

Antara Mukherjee
Department of Mathematics and Computer Science, The Citadel, Charleston, SC, United States

Abstract


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.