A general splitting principle on RCD spaces and applications to spaces with positive spectrum
Metric Geometry
2023-12-12 v1 Differential Geometry
Abstract
In this paper we develop a general `analytic' splitting principle for RCD spaces: we show that if there is a function with suitable Laplacian and Hessian, then the space is (isomorphic to) a warped product. Our result covers most of the splitting-like results currently available in the literature about RCD spaces. We then apply it to extend to the non-smooth category some structural property of Riemannian manifolds obtained by Li and Wang.
Cite
@article{arxiv.2312.06252,
title = {A general splitting principle on RCD spaces and applications to spaces with positive spectrum},
author = {Nicola Gigli and Fabio Marconi},
journal= {arXiv preprint arXiv:2312.06252},
year = {2023}
}