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.
A General Splitting Principle on RCD Spaces and Applications to Spaces with Positive Spectrum / Gigli, N., Marconi, F.. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 35:11(2025). [10.1007/s12220-025-02135-9]
A General Splitting Principle on RCD Spaces and Applications to Spaces with Positive Spectrum
Gigli, Nicola;Marconi, Fabio
2025-01-01
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.| File | Dimensione | Formato | |
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