Any isometry between the spheres of absolutely smooth $2$-dimensional Banach spaces is linear
Functional Analysis
2021-11-01 v4 Classical Analysis and ODEs
Differential Geometry
Metric Geometry
Abstract
We prove that any isometry between the unit spheres of -smooth (more generally, absolutely smooth) smooth Banach spaces extends to a linear isometry of the Banach spaces. This answers the famous Tingley's problem in the class of absolutely smooth -dimensional Banach spaces.
Cite
@article{arxiv.1911.03767,
title = {Any isometry between the spheres of absolutely smooth $2$-dimensional Banach spaces is linear},
author = {Taras Banakh},
journal= {arXiv preprint arXiv:1911.03767},
year = {2021}
}
Comments
22 pages