Growth of Leaves of a Foliation on a Manifold

Question

Let $M$ be a (Real or Complex) Manifold of dimension $m$ and $\mathcal{F}$ a Foliation of dimension $k$, $1 \leq k \leq m-1$, on $M$.

I am actually looking for highly recommended references on the concept of Growth of Leaves.

I do appreciate any help could be provided.

Thanks in advance.

Answer 1

Here are three starting points:

For the relation with growth of groups, Milnor's papers "A note on curvature and fundamental group" and "Growth of finitely generated solvable groups" are worth having a look. See also Plante and Thurston's paper "Polynomial Growth in Holonomy Groups of Foliations".

For the relation with growth of (ergodic) equivalence relations Hurder and Katok's paper "Ergodic Theory And Weil Measures For Foliations" is valuable.

A good textbook account of growth of foliations is Ch. 12 of Candel and Conlon's book Foliations I.