Complexity of distances: Reductions of distances between metric and Banach spaces

0557873 - MÚ 2023 RIV IL eng J - Journal Article
Cúth, M. - Doucha, Michal - Kurka, Ondřej
Complexity of distances: Reductions of distances between metric and Banach spaces.
Israel Journal of Mathematics. Roč. 248, č. 1 (2022), s. 383-439. ISSN 0021-2172. E-ISSN 1565-8511
R&D Projects: GA ČR(CZ) GX20-31529X
Institutional support: RVO:67985840
Keywords : intrinsic flat * manifolds
OECD category: Pure mathematics
Impact factor: 1, year: 2022
Method of publishing: Limited access
https://doi.org/10.1007/s11856-022-2305-7

We show that all the standard distances from metric geometry and functional analysis, such as Gromov-Hausdorff distance, Banach-Mazur distance, Kadets distance, Lipschitz distance, Net distance, and Hausdorff-Lipschitz distance have all the same complexity and are reducible to each other in a precisely defined way. This is done in terms of descriptive set theory and is a part of a larger research program initiated by the authors in [8]. The paper is however targeted also to specialists in metric geometry and geometry of Banach spaces.
Permanent Link: http://hdl.handle.net/11104/0331719