Journal of the Ramanujan Mathematical Society

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Isoperimetric Inequalities Using Varopoulos Transport


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

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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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  • Isoperimetric Inequalities Using Varopoulos Transport

Abstract Views: 257  |  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.