The splitting theorem in non-smooth context
Metric Geometry
2026-04-30 v2 Differential Geometry
Abstract
We prove that an infinitesimally Hilbertian CD(0,N) space containing a line splits as the product of and an infinitesimally Hilbertian CD(0,N-1) space. By `infinitesimally Hilbertian' we mean that the Sobolev space , which in general is a Banach space, is an Hilbert space. When coupled with a curvature-dimension bound, this condition is known to be stable with respect to measured Gromov-Hausdorff convergence.
Keywords
Cite
@article{arxiv.1302.5555,
title = {The splitting theorem in non-smooth context},
author = {Nicola Gigli},
journal= {arXiv preprint arXiv:1302.5555},
year = {2026}
}
Comments
Final version as appeared in Memoirs of the AMS