[1302.5555] The splitting theorem in non-smooth context Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Metric Geometry arXiv:1302.5555 (math) [Submitted on 22 Feb 2013 ( v1 ), last revised 29 Apr 2026 (this version, v2)] Title: The splitting theorem in non-smooth context Authors: Nicola Gigli View a PDF of the paper titled The splitting theorem in non-smooth context, by Nicola Gigli View PDF HTML (experimental) Abstract: We prove that an infinitesimally Hilbertian CD(0,N) space containing a line splits as the product of $R$ and an infinitesimally Hilbertian CD(0,N-1) space. By `infinitesimally Hilbertian' we mean that the Sobolev space $W^{1,2}(X,d,m)$, which in general is a Banach space, is an Hilbert space. When coupled with a curvature-dimension bound, this condition is known to be stable with respect to measured Gromov-Hausdorff convergence. Comments: Final version as appeared in Memoirs of the AMS Subjects: Metric Geometry (math.MG) ; Differential Geometry (math.DG) MSC classes: 53Cxx, 51Fxx Cite as: arXiv:1302.5555 [math.MG] (or arXiv:1302.5555v2 [math.MG] for this version) https://doi.org/10.48550/arXiv.1302.5555 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Nicola Gigli [ view email ] [v1] Fri, 22 Feb 2013 11:28:54 UTC (95 KB) [v2] Wed, 29 Apr 2026 10:28:05 UTC (108 KB) Full-text links: Access Paper: View a PDF of the paper titled The splitting theorem in non-smooth context, by Nicola Gigli View PDF HTML (experimental) TeX Source view license Current browse context: math.MG < prev | next > new | recent | 2013-02 Change to browse by: math math.DG References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from