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An overview of the proof of the splitting theorem in spaces with non-negative Ricci curvature.(English)Zbl 1310.53031

Summary: In the recent paper [the author, “The splitting theorem in non-smooth context”, Preprint,arXiv:1302.5555] the Cheeger-Colding-Gromoll splitting theorem has been generalized to the abstract class of metric measure spaces with Riemannian Ricci curvature bounded from below, the analysis being based on some definitions and results contained in [the author, “On the differential structure of metric measure spaces and applications”, Preprint,arXiv:1205.6622]. These two papers add up to almost 200 pages and as such they are not suitable for getting a quick idea of the techniques used to work in the non-smooth setting. This is the aim of this note: to provide an as short as possible yet comprehensive proof of the splitting in such abstract framework.

MSC:

53C20 Global Riemannian geometry, including pinching
52-02 Research exposition (monographs, survey articles) pertaining to convex and discrete geometry
53C23 Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
53C70 Direct methods (\(G\)-spaces of Busemann, etc.)

Cite

References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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