Packing and doubling in metric spaces with curvature bounded above
Metric Geometry
2021-02-16 v2
Abstract
We study locally compact, locally geodesically complete, locally CAT(k) spaces (GCBA(k)-spaces). We prove a Croke-type local volume estimate only depending on the dimension of these spaces. We show that a local doubling condition, with respect to the natural measure, implies pure-dimensionality. Then, we consider GCBA(k)-spaces satisfying a uniform packing condition at some fixed scale or a doubling condition at arbitrarily small scale, and prove several compactness results with respect to pointed Gromov-Hausdorff convergence. Finally, as a particular case, we study convergence and stability of M^k-complexes with bounded geometry.
Keywords
Cite
@article{arxiv.2009.12099,
title = {Packing and doubling in metric spaces with curvature bounded above},
author = {Nicola Cavallucci and Andrea Sambusetti},
journal= {arXiv preprint arXiv:2009.12099},
year = {2021}
}