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arXiv · 2312.06252

A general splitting principle on RCD spaces and applications to spaces with positive spectrum

Nicola Gigli·Fabio Marconi
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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.

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Nicola Gigli, Fabio Marconi. 2023-12-11. A general splitting principle on RCD spaces and applications to spaces with positive spectrum. https://arxiv.org/abs/2312.06252

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