11 problems

Let $\Gamma$ be a finitely generated discrete subgroup of $\operatorname{PSL}_2(\mathbb{C})$, and let $\Lambda$ be its limit set in $\mathbb S^2$. Ahlfors measure conjecture. The l…

Let $G$ be a group that is not virtually abelian, let ${\cal D}(G)$ be the deformation space of representations of $G$, and let $\{\rho_j\}\subset{\cal D}(G)$ converge algebraicall…

Let $M$ be the state manifold of a differentially positive system, let $\flow$ denote its flow, and let $\omega(x)$ be the $\omega$-limit set of the orbit through $x$. A point is u…

Let $G_{6,3}=\langle a_0,\cdots,a_5\mid a_i^3=id,\ a_ia_{i+1}=a_{i+1}a_i,\ i\in\mathbb{Z}/6\mathbb{Z}\rangle$ be the hyperbolic group with boundary the Menger curve, and let…

Let $\Delta_{4,4,4;7}<\mathbf{PU}(2,1)$ be Schwartz's arithmetic, geometrically finite, discrete image group arising from an unfaithful representation of a triangle group. Schwartz…

Let $G$) be a Kleinian group whose convex hull $H(L(G))$ admits a uniformly distributed set $X$. For $s>0$ and $z inmathbb{B}^{n+1}$, define the extended Poincaré series … Let…

Cannon–Thurston conjecture. The inclusion $\tilde{i}:\widetilde{S^h}\rightarrow\mathbb{H}^3$ extends continuously to the boundary.

Let $a=\zeta_k$ and $x=\zeta_m$ be primitive roots of unity, with $m\geq3$. Limit-point conjecture. The continued fraction $K_a(x)$ converges exactly when … and hence exactly when…

In Poincaré's setting, consider the limit curve of a discrete group generated by inversions in a simple closed chain of externally tangent circles. A point of the limit curve is pa…

Let $\Gamma$ be a non-elementary Kleinian group acting on $\mathbb H^n$ for some $n\ge 2$, and let $\Phi$ and $\Theta$ be non-elementary subgroups of $\Gamma$. For a subgroup $H$ o…

Inverse integrating factor regularity conjecture. The same conclusion should remain valid when $V$ is merely of class $\mathcal{C}^1$; that is,