Removable singularities for nonlocal minimal graphs

[2501.14299] Removable singularities for nonlocal minimal graphs Skip to main content Search Submit Donate Log in Mathematics > Differential Geometry arXiv:2501.14299 (math) [Submitted on 24 Jan 2025 ( v1 ), last revised 30 Jan 2026 (this version, v2)] Title: Removable singularities for nonlocal minimal graphs Authors: Minhyun Kim View PDF Abstract: We prove the removable singularity theorem for nonlocal minimal graphs. Specifically, we show that any nonlocal minimal graph in $\Omega \setminus K$, where $\Omega \subset \mathbb{R}^n$ is an open set and $K \subset \Omega$ is a compact set of $(s, 1)$-capacity zero, is indeed a nonlocal minimal graph in all of $\Omega$. Comments: 16 pages Subjects: Differential Geometry (math.DG) ; Analysis of PDEs (math.AP) MSC classes: 53A10, 49Q05, 35J60 Cite as: arXiv:2501.14299 [math.DG] (or arXiv:2501.14299v2 [math.DG] for this version) https://doi.org/10.48550/arXiv.2501.14299 Focus to learn more arXiv-issued DOI via DataCite Journal reference: J. Geom. Anal. 36 (2026), no. 3, Paper No. 96, 19 pp Related DOI : https://doi.org/10.1007/s12220-026-02344-w Focus to learn more DOI(s) linking to related resources Submission history From: Minhyun Kim [ view email ] [v1] Fri, 24 Jan 2025 07:44:27 UTC (14 KB) [v2] Fri, 30 Jan 2026 20:48:42 UTC (15 KB) Full-text links: Access Paper: View PDF TeX Source view license Current browse context: math.DG < prev | next > new | recent | 2025-01 Change to browse by: math math.AP References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation 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)

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