2020

Jones, Rebekah; Lahti, Panu; Shanmugalingam, Nageswari

We generalize a result of Kelly [17] to the setting of Ahlfors Q-regular metric measure spaces supporting a 1-Poincare inequality. It is shown that if X and Y are two Ahlfors Q-regular spaces supporting a 1-Poincare inequality and f : X -> Y is a quasiconformal mapping, then the Q/ (Q - 1)-modulus of the collection of measures H(Q-1)left perpendicular Sigma E corresponding to any collection of sets E subset of X of finite perimeter is quasi-preserved by f. We also show that for Q/ (Q - 1)-modulus almost every Sigma E, f (E) is also of finite perimeter. Even in the standard Euclidean setting our results are more general than that of Kelly, and hence are new even in that setting.