3 problems

Let $\mathcal{X}$ and $\mathcal{Y}$ be finite alphabets, let $d(x,y)$ be a distortion measure, let $P$ be a probability distribution on $\mathcal{X}$, and let $R(\Delta|P)$ denote…

Finite-height subgroup conjecture. If $H$ has finite height in $G$, then $H$ is quasi-convex in $G$.

Let $G$ be a group hyperbolic relative to the peripheral system $\mathcal{P}=\{P_1,\ldots,P_n\}$. Suppose that hyperbolic groups are residually finite, and that each $P_i$ is finit…