Warped quasi-asymptotically conical Calabi-Yau metrics

[2308.02155] Warped quasi-asymptotically conical Calabi-Yau metrics Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Differential Geometry arXiv:2308.02155 (math) [Submitted on 4 Aug 2023 ( v1 ), last revised 14 Apr 2026 (this version, v3)] Title: Warped quasi-asymptotically conical Calabi-Yau metrics Authors: Ronan J. Conlon , Frédéric Rochon View a PDF of the paper titled Warped quasi-asymptotically conical Calabi-Yau metrics, by Ronan J. Conlon and Fr\'ed\'eric Rochon View PDF HTML (experimental) Abstract: We construct many new examples of complete Calabi-Yau metrics of maximal volume growth on certain smoothings of Cartesian products of Calabi-Yau cones with smooth cross-sections. A detailed description of the geometry at infinity of these metrics is given in terms of a compactification by a manifold with corners obtained through the notion of weighted blow-up for manifolds with corners. A key analytical step in the construction of these Calabi-Yau metrics is to derive good mapping properties of the Laplacian on some suitable weighted Hölder spaces. Our methods also produce singular Calabi-Yau metrics with an isolated conical singularity modelled on a Calabi-Yau cone distinct from the tangent cone at infinity, in particular yielding a transition behavior between different Calabi-Yau cones as conjectured by Yang Li. This is used to exhibit many examples where the tangent cone at infinity does not uniquely specify a complete Calabi-Yau metric with exact Kähler form. Comments: 64 pages, corrected some typos Subjects: Differential Geometry (math.DG) ; Algebraic Geometry (math.AG); Analysis of PDEs (math.AP) MSC classes: 53C55, 58J05 Cite as: arXiv:2308.02155 [math.DG] (or arXiv:2308.02155v3 [math.DG] for this version) https://doi.org/10.48550/arXiv.2308.02155 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Frederic Rochon [ view email ] [v1] Fri, 4 Aug 2023 06:27:27 UTC (55 KB) [v2] Wed, 13 Dec 2023 19:27:07 UTC (71 KB) [v3] Tue, 14 Apr 2026 20:44:55 UTC (72 KB) Full-text links: Access Paper: View a PDF of the paper titled Warped quasi-asymptotically conical Calabi-Yau metrics, by Ronan J. Conlon and Fr\'ed\'eric Rochon View PDF HTML (experimental) TeX Source view license Current browse context: math.DG < prev | next > new | recent | 2023-08 Change to browse by: math math.AG math.AP 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

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