[2211.02124] The Number of Singularities in the Intersections of Convex Planar Translates Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Geometric Topology arXiv:2211.02124 (math) This paper has been withdrawn by Cameron Strachan Mr. [Submitted on 3 Nov 2022 ( v1 ), last revised 30 Apr 2026 (this version, v2)] Title: The Number of Singularities in the Intersections of Convex Planar Translates Authors: Cameron Strachan View a PDF of the paper titled The Number of Singularities in the Intersections of Convex Planar Translates, by Cameron Strachan No PDF available, click to view other formats Abstract: This purpose of this paper is to prove the following result: let phi be a strictly convex, smooth, convex body in the Euclidean plane, if the intersection of n translates of phi has a non-empty interior, and all of the translates contribute to the intersection, then the intersection of these n translates will have exactly n points of singularity along its boundary. Furthermore this result is sharp, in the sense that, removing any one of the assumptions from our statement will render the result unable to hold in general. Comments: This article has been superseded by arXiv:2211.16621 Subjects: Geometric Topology (math.GT) Cite as: arXiv:2211.02124 [math.GT] (or arXiv:2211.02124v2 [math.GT] for this version) https://doi.org/10.48550/arXiv.2211.02124 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Cameron Strachan Mr. [ view email ] [v1] Thu, 3 Nov 2022 20:00:41 UTC (1,191 KB) [v2] Thu, 30 Apr 2026 11:25:00 UTC (1 KB) (withdrawn) Full-text links: Access Paper: View a PDF of the paper titled The Number of Singularities in the Intersections of Convex Planar Translates, by Cameron Strachan Withdrawn No license for this version due to withdrawn Current browse context: math.GT < prev | next > new | recent | 2022-11 Change to browse by: math 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