Logarithmic Brunn--Minkowski Inequality under $n-2$ Reflection Symmetries

[2608.20730] Logarithmic Brunn--Minkowski Inequality under $n-2$ Reflection Symmetries Skip to main content Search Submit Donate Log in Mathematics > Metric Geometry arXiv:2608.20730 (math) [Submitted on 21 Aug 2026 ( v1 ), last revised 28 Sep 2026 (this version, v3)] Title: Logarithmic Brunn--Minkowski Inequality under $n-2$ Reflection Symmetries Authors: XiaoRui Lu View PDF HTML (experimental) Abstract: For origin-symmetric convex bodies in $\R^n$ invariant under $n-2$ orthogonal hyperplanes reflections, we establish the logarithmic Brunn--Minkowski inequality and classify all equality cases without regularity assumptions. We derive the logarithmic Minkowski inequality and rigidity for cone-volume measures, including an explicit classification for bodies of revolution and uniqueness for simplicial polytopes in the prescribed symmetry class. Subjects: Metric Geometry (math.MG) ; Analysis of PDEs (math.AP); Differential Geometry (math.DG) Cite as: arXiv:2608.20730 [math.MG] (or arXiv:2608.20730v3 [math.MG] for this version) https://doi.org/10.48550/arXiv.2608.20730 Focus to learn more arXiv-issued DOI via DataCite Submission history From: XiaoRui Lu [ view email ] [v1] Fri, 21 Aug 2026 04:22:15 UTC (21 KB) [v2] Thu, 27 Aug 2026 05:57:39 UTC (21 KB) [v3] Mon, 28 Sep 2026 14:10:21 UTC (20 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.MG < prev | next > new | recent | 2026-08 Change to browse by: math math.AP math.DG 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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