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1 vote
1 answer
149 views

Conull subspace containing orbit of an (ergodically acting) group

I should probably start with a warning that this is my first post in this board and that I am sorry, if it is not up to standards. It would be great, if you could let me know how to improve the post. ...
2 votes
0 answers
85 views

Banach density of a sequence of spheres in a virtually nilpotent group

Let $G$ be a finitely-generated group of polynomial growth equipped with the word metric (with respect to a fixed symmetric generating set). Let \begin{equation*} A = \left\{ g \in G: |g| = mn, n \...
3 votes
0 answers
383 views

Discontinuity of Radon-Nikodym derivative for Patterson-Sullivan measures for word metrics on Gromov hyperbolic groups

Let $\Gamma$ be a Gromov hyperbolic group coming endowed with a word metric coming from some finite generating set. Let $\nu$ be an associated Patterson-Sullivan measure (quasi-conformal density). I ...
6 votes
0 answers
383 views

When is a word metric on a CAT(-1) group a bounded distance from the orbit map of an isometric action on some CAT(-k) metric space?

Let $\Gamma$ be a group admitting a discrete and cocompact action on a CAT(-1) space. Let $d$ a word metric on $\Gamma$ coming from some finite set of generators. My question is: Does there exist a ...