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Results tagged with hyperbolic-geometry
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user 80571
5
votes
1
answer
244
views
Geodesics (with the same limit point) in a surface group of genus two
Consider a discrete Gromov-hyperbolic group $\Gamma$ (and its Cayley graph
$\mathcal{G}$ w.r.t. some generating set). The notion of
Gromov-boundary, indicated with $\partial\Gamma$,
is naturally as …
- 2,371
2
votes
1
answer
214
views
Subsets of the boundary of a surface group
Consider the surface group $\Gamma=\langle a,b,c,d\mid [a,b][c,d]=1\rangle$: it is a Gromov hyperbolic group; its Gromov boundary $\partial\Gamma$ is homeomorphic to $S^1$ (the unit circle).
I would l …
- 31.2k
2
votes
0
answers
135
views
Extending continuous functions from $\partial X$ to $X\cup \partial X$
Consider a proper geodesic hyperbolic space $X$ (in the sense of Gromov). Let $\partial X$ be its Gromov boundary. Consider a complex-valued continuous function on the boundary $f\colon\partial X\to\m …
- 329