Isoperimetric inequalities for related conformal maps.

Some inequalities related to isoperimetric inequalities with partial free boundary

The main purpose of this paper is to prove a sharp Sobolev inequality in an exterior of a convex bounded domain. There are two ingredients in the proof: One is the observation of some new isoperimetric inequalities with partial free boundary, and the other is an integral inequality (due to Duff [9]) for any nonnegative function under Schwarz equimeasurable rearrangement. These ingredients also ...

Isoperimetric inequalities for convex hulls and related questions

We consider the problem of maximizing the Lebesgue measure of the convex hull of a connected compact set of prescribed onedimensional Hausdorff measure. In dimension two, we prove that the only solutions are semicircles. In higher dimension, we prove some isoperimetric inequalities for the convex hull of connected sets, we focus on a classical open problem and we discuss a new possible approach.

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