3 problems

Let $\mathbf{P}=(p_1,\dots,p_5)$ be a pentagon, and let $S_\mathbf{P}$ and $L_\mathbf{P}$ denote the symmedian and hyperbolic barycenters, respectively. For cyclically indexed vert…

Geometric convergence conjecture. The geometric convergence rate at equation $$ may still hold when $m>2$.

Let $(M,d)$ be a metric space, let $P$ be a probability measure for which empirical barycenters $x_n$ and a barycenter $x^*$ are defined, and consider the barycenter problem with…