Metric Spaces of Arbitrary Finitely-Generated Scaling Group

Abstract: For a metric space

X

with a compatible measure

m u

, Genevois and Tessera defined the Scaling Group of

(X, m u)

as the subgroup

G a m m a

of

m a t h b b R_{> 0}

of positive real numbers

g a m m a

for which there are quasi-isometries of

X

coarsely scaling

m u

by a factor of

g a m m a

. We show that for any finitely generated subgroup

G a m m a

of

m a t h b b R_{> 0}

there exists a space

N_{G} a m m a

, bi-Lipschitz equivalent to a graph of finite degree, with scaling group

G a m m a

.

This page was built for publication: Metric Spaces of Arbitrary Finitely-Generated Scaling Group