Alexandrov-Fenchel type inequalities with convex weight in space forms

[2412.08923] Alexandrov-Fenchel type inequalities with convex weight in space forms Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Differential Geometry arXiv:2412.08923 (math) [Submitted on 12 Dec 2024] Title: Alexandrov-Fenchel type inequalities with convex weight in space forms Authors: Kwok-Kun Kwong , Yong Wei View a PDF of the paper titled Alexandrov-Fenchel type inequalities with convex weight in space forms, by Kwok-Kun Kwong and Yong Wei View PDF HTML (experimental) Abstract: In this paper, we derive new sharp weighted Alexandrov-Fenchel and Minkowski inequalities for smooth, closed hypersurfaces under various convexity assumptions in Euclidean, spherical, and hyperbolic spaces. These inequalities extend classical results by incorporating weights given by convex, non-decreasing positive functions, which are otherwise arbitrary. Our approach gives rise to a broad family of geometric inequalities, as each convex, non-decreasing function yields a corresponding inequality, providing considerable flexibility. Comments: 21 pages Subjects: Differential Geometry (math.DG) ; Analysis of PDEs (math.AP) Cite as: arXiv:2412.08923 [math.DG] (or arXiv:2412.08923v1 [math.DG] for this version) https://doi.org/10.48550/arXiv.2412.08923 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Annali di Matematica Pura ed Applicata 2026 Related DOI : https://doi.org/10.1007/s10231-026-01663-7 Focus to learn more DOI(s) linking to related resources Submission history From: Yong Wei [ view email ] [v1] Thu, 12 Dec 2024 04:14:40 UTC (18 KB) Full-text links: Access Paper: View a PDF of the paper titled Alexandrov-Fenchel type inequalities with convex weight in space forms, by Kwok-Kun Kwong and Yong Wei View PDF HTML (experimental) TeX Source view license Current browse context: math.DG < prev | next > new | recent | 2024-12 Change to browse by: math math.AP 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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