Local Variational Properties of Non-degenerate Free Boundary Minimal Hypersurfaces

[2605.25585] Local Variational Properties of Non-degenerate Free Boundary Minimal Hypersurfaces Skip to main content Search Submit Donate Log in Mathematics > Differential Geometry arXiv:2605.25585 (math) [Submitted on 25 May 2026 ( v1 ), last revised 22 Aug 2026 (this version, v3)] Title: Local Variational Properties of Non-degenerate Free Boundary Minimal Hypersurfaces Authors: Xiaoxiang Jiao , Qinhan Zhao , Hangyue Zhu View PDF HTML (experimental) Abstract: We establish local variational characterizations of non-degenerate free-boundary minimal hypersurfaces in compact Riemannian manifolds with boundary. For a two-sided strictly stable hypersurface, we show that it is the unique mass minimizer in its relative homology class, both in a small tubular and flat-neighborhood. As an application, for generic metrics in dimensions $3\le n+1\le 7$, we show that the first free-boundary width is realized by a multiplicity-one hypersurface of Morse index one. For an orientable non-degenerate free-boundary hypersurface of Morse index $k>0$, we construct a canonical local $k$-parameter family and obtain a local min--max characterization. Subjects: Differential Geometry (math.DG) Cite as: arXiv:2605.25585 [math.DG] (or arXiv:2605.25585v3 [math.DG] for this version) https://doi.org/10.48550/arXiv.2605.25585 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Hangyue Zhu [ view email ] [v1] Mon, 25 May 2026 08:34:58 UTC (38 KB) [v2] Wed, 29 Jul 2026 10:20:23 UTC (331 KB) [v3] Sat, 22 Aug 2026 03:51:20 UTC (45 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.DG < prev | next > new | recent | 2026-05 Change to browse by: math 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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