2021/04/07 by Anders Karlsson · 1 citation
Physics and Astronomy · Mathematics · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities
paper · doi:10.1016/j.jfa.2021.109030
It is observed that a natural analog of the Hahn-Banach theorem is valid for metric functionals but fails for horofunctions. Several statements of the existence of invariant metric functionals for individual isometries and 1-Lipschitz maps are proved. Various other definitions, examples and facts are pointed out related to this topic. In particular it is shown that the metric (horofunction) boundary of every infinite Cayley graphs contains at least two points.