Limits of manifolds with boundary I

[2406.00970] Limits of manifolds with boundary I Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Differential Geometry arXiv:2406.00970 (math) [Submitted on 3 Jun 2024 ( v1 ), last revised 11 Apr 2026 (this version, v4)] Title: Limits of manifolds with boundary I Authors: Takao Yamaguchi , Zhilang Zhang View a PDF of the paper titled Limits of manifolds with boundary I, by Takao Yamaguchi and 1 other authors View PDF HTML (experimental) Abstract: In this paper, we develop the infinitesimal geometry of the limit spaces of compact Riemannian manifolds with boundary, where we assume lower bounds on the sectional curvatures of manifolds and boundaries and the second fundamental forms of boundaries and an upper diameter bound. We mainly focus on the case when inradii of manifolds are uniformly bounded away from zero. In this case, many limit spaces have wild geometry, which arise as the boundary singular points of the limit spaces. We determine the infinitesimal structure at those boundary singular points. We also determine the Hausdorff dimensions of the boundary singular sets. Comments: 81 pages, 11 figures, 4 tables. Mainly Sections 5 and 8 were modified Subjects: Differential Geometry (math.DG) ; Metric Geometry (math.MG) MSC classes: 53C20 Cite as: arXiv:2406.00970 [math.DG] (or arXiv:2406.00970v4 [math.DG] for this version) https://doi.org/10.48550/arXiv.2406.00970 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Takao Yamaguchi [ view email ] [v1] Mon, 3 Jun 2024 03:48:02 UTC (75 KB) [v2] Tue, 20 Aug 2024 03:09:05 UTC (82 KB) [v3] Fri, 4 Apr 2025 07:08:44 UTC (65 KB) [v4] Sat, 11 Apr 2026 07:51:23 UTC (77 KB) Full-text links: Access Paper: View a PDF of the paper titled Limits of manifolds with boundary I, by Takao Yamaguchi and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.DG < prev | next > new | recent | 2024-06 Change to browse by: math math.MG 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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