5 problems

Linear growth conjecture. The quantity $\lambda\left(\prod_{i=1}^n\mathcal{F}(A_i)\right)$ is equivalent to $n$ as $n\to\infty$; that is, it grows linearly in $n$ up to multiplicat…

Uniform lattice conjecture. Every lattice $\Gamma\subset M$ with the $\mathcal{LE}$ is uniform. The source places this definition immediately before the conjectural discussion, but…

Let $X$ and $Y$ be Hadamard manifolds, let $C<1$, and let $\mathcal{L}_{X,Y}(C)$ denote the optimal Lipschitz constant for extending every $C$-Lipschitz map from a subset of $X$ to…

Let $C<1$. For Hadamard manifolds $X$ and $Y$ satisfying … write $\mathcal{L}_{X,Y}(C)$ for the optimal Lipschitz constant needed to extend every $C$-Lipschitz map from a subset of…

Generalization conjecture. The assumption that $X$ is locally compact can be dropped from the theorem asserting that every Lipschitz map from a closed subset of $X$ to a metric tre…