[2608.14431] Classification of compact Lagrangian self-similar submanifolds with Legendrian capillary boundary in the unit ball Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Differential Geometry arXiv:2608.14431 (math) [Submitted on 14 Aug 2026] Title: Classification of compact Lagrangian self-similar submanifolds with Legendrian capillary boundary in the unit ball Authors: Dong Gao , Yong Luo , Hui Ma , Jiabin Yin View a PDF of the paper titled Classification of compact Lagrangian self-similar submanifolds with Legendrian capillary boundary in the unit ball, by Dong Gao and 3 other authors View PDF HTML (experimental) Abstract: We classify smooth compact connected Lagrangian immersions $X$ in the closed unit ball of $\C^n$, $n\ge2$, satisfying $H+\varepsilon X^\perp=0$, $\varepsilon\in\{-1,0,1\}$, with Legendrian boundary on the unit sphere and constant contact angle on each connected component. We prove that the boundary has at most two connected components. When the boundary is connected, $X$ is a diffeomorphism onto an equatorial Lagrangian $n$-disk. When the boundary has two components, $X$ splits globally as $X(s,p)=\gamma(s)\psi(p)$, where $\psi$ is a compact minimal Legendrian immersion in the unit sphere and $\gamma$ is an Anciaux profile with a unique radial minimum. The two contact angles are supplementary. In complex dimension two, every non-disk solution is a finite cover of a Lagrangian catenoid segment for $\varepsilon=0$ or of a rotational Anciaux annulus for $\varepsilon=\pm1$. In higher complex dimensions, iterated Calabi suspensions produce families whose minimal Legendrian links have nontrivial topology. Comments: All comments are welcome Subjects: Differential Geometry (math.DG) Cite as: arXiv:2608.14431 [math.DG] (or arXiv:2608.14431v1 [math.DG] for this version) https://doi.org/10.48550/arXiv.2608.14431 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Yong Luo [ view email ] [v1] Fri, 14 Aug 2026 16:12:50 UTC (32 KB) Full-text links: Access Paper: View a PDF of the paper titled Classification of compact Lagrangian self-similar submanifolds with Legendrian capillary boundary in the unit ball, by Dong Gao and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.DG < prev | next > new | recent | 2026-08 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