Isoperimetric inequalities for infinite hyperplane systems

Isoperimetric inequalities for nilpotent groups

We prove that every finitely generated nilpotent group of class c admits a polynomial isoperimetric function of degree c+1 and a linear upper bound on its filling length function. 1991 Mathematics Subject Classification: 20F05, 20F32, 57M07

Isoperimetric inequalities for soluble groups

We approach the question of which soluble groups are automatic. We describe a class of nilpotent-by-abelian groups which need to be studied in order to answer this question. We show that the nilpotent-by-cyclic groups in this class have exponential isoperimetric inequality and so cannot be automatic.

Isoperimetric inequalities for Random Walks

Isoperimetric inequalities for minimal graphs

Based on Markvorsen and Palmer work on mean time exit and isoperimetric inequalities we establish slightly better isoperimetric inequalities and mean time exit estimates for minimal graphs in N × R. We also prove isoperimetric inequalities for submanifolds of Hadamard spaces with tamed second fundamental form. Mathematics Subject Classification: (2000): Primary 53C42; Secondary 53A10

Lp AFFINE ISOPERIMETRIC INEQUALITIES

Affine isoperimetric inequalities compare functionals, associated with convex (or more general) bodies, whose ratios are invariant under GL(n)-transformations of the bodies. These isoperimetric inequalities are more powerful than their better-known relatives of a Euclidean flavor. To be a bit more specific, this article deals with inequalities for centroid and projection bodies. Centroid bodies...