Strengthened inequalities for the mean width and the $\ell$-norm of origin symmetric convex bodies

[2410.11460] Strengthened inequalities for the mean width and the $\ell$-norm of origin symmetric convex bodies Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Metric Geometry arXiv:2410.11460 (math) [Submitted on 15 Oct 2024] Title: Strengthened inequalities for the mean width and the $\ell$-norm of origin symmetric convex bodies Authors: Károly J. Böröczky , Ferenc Fodor , Daniel Hug View a PDF of the paper titled Strengthened inequalities for the mean width and the $\ell$-norm of origin symmetric convex bodies, by K\'aroly J. B\"or\"oczky and 2 other authors View PDF HTML (experimental) Abstract: Barthe, Schechtman and Schmuckenschläger proved that the cube maximizes the mean width of symmetric convex bodies whose John ellipsoid (maximal volume ellipsoid contained in the body) is the Euclidean unit ball, and the regular crosspolytope minimizes the mean width of symmetric convex bodies whose Löwner ellipsoid is the Euclidean unit ball. Here we prove close to be optimal stronger stability versions of these results, together with their counterparts about the $\ell$-norm based on Gaussian integrals. We also consider related stability results for the mean width and the $\ell$-norm of the convex hull of the support of even isotropic measures on the unit sphere. Subjects: Metric Geometry (math.MG) MSC classes: 52A40 (Primary) 52A38, 52B12, 26D15 (Secondary) Cite as: arXiv:2410.11460 [math.MG] (or arXiv:2410.11460v1 [math.MG] for this version) https://doi.org/10.48550/arXiv.2410.11460 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Math. Ann. 393 (2025), 271-316 Related DOI : https://doi.org/10.1007/s00208-025-03228-0 Focus to learn more DOI(s) linking to related resources Submission history From: Ferenc Fodor [ view email ] [v1] Tue, 15 Oct 2024 10:08:08 UTC (31 KB) Full-text links: Access Paper: View a PDF of the paper titled Strengthened inequalities for the mean width and the $\ell$-norm of origin symmetric convex bodies, by K\'aroly J. B\"or\"oczky and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.MG < prev | next > new | recent | 2024-10 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

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