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

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arxiv 2312.06252 v1 pith:W4DEQCCU submitted 2023-12-11 math.MG math.DG

Nicola Gigli , Fabio Marconi This is my paper · ORCID
classification math.MGmath.DG
keywords spacesgeneralprinciplesplittingthenanalyticapplicationsapply
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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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  1. Warped products over one-dimensional base spaces and the RCD condition

    math.DG 2025-06 conditional novelty 7.0 of 10

    An N-warped product over a one-dimensional base satisfies the RCD(KN,N+1) curvature condition exactly when the warping function is K-concave, obeys a boundary condition, and the fiber satisfies a related RCD condition.

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