English

Products of hyperbolic spaces

Metric Geometry 2024-10-30 v3

Abstract

The class of uniformly smooth hyperbolic spaces was recently introduced by the first author as a common generalization of both CAT(0) spaces and uniformly smooth Banach spaces, in a way that Reich's theorem on resolvent convergence could still be proven. We define products of such spaces, showing that they are reasonably well-behaved. In this manner, we provide the first example of a space for which Reich's theorem holds and which is neither a CAT(0) space, nor a convex subset of a normed space.

Keywords

Cite

@article{arxiv.2408.14093,
  title  = {Products of hyperbolic spaces},
  author = {Pedro Pinto and Andrei Sipos},
  journal= {arXiv preprint arXiv:2408.14093},
  year   = {2024}
}
R2 v1 2026-06-28T18:23:41.818Z