Sectional curvature and matrix displacement convexity

[2509.23399] Sectional curvature and matrix displacement convexity Skip to main content Search Submit Donate Log in Mathematics > Differential Geometry arXiv:2509.23399 (math) [Submitted on 27 Sep 2025 ( v1 ), last revised 26 Aug 2026 (this version, v2)] Title: Sectional curvature and matrix displacement convexity Authors: Gautam Aishwarya , Liran Rotem , Yair Shenfeld View PDF HTML (experimental) Abstract: We show that the sectional curvature of a Riemannian manifold is nonnegative if, and only if, the entropy tensor is matrix displacement convex. As an application, under the assumption of nonnegative sectional curvature, we obtain intrinsic dimensional strengthenings of the HWI inequality, the evolution variational inequality, and the corresponding Wasserstein contraction along heat flows. Moreover, we show that the intrinsic dimensional Wasserstein contraction inequality in fact characterizes nonnegative sectional curvature. Comments: Two new results added: (i) Intrinsic dimensional HWI (Theorem 1.11), (ii) intrinsic dimensional Wasserstein contractions characterize nonnegative sectional curvature (Theorem 1.9) Subjects: Differential Geometry (math.DG) ; Analysis of PDEs (math.AP); Probability (math.PR) MSC classes: 35K05, 58J35, 53C21, 49Q22 Cite as: arXiv:2509.23399 [math.DG] (or arXiv:2509.23399v2 [math.DG] for this version) https://doi.org/10.48550/arXiv.2509.23399 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Gautam Aishwarya [ view email ] [v1] Sat, 27 Sep 2025 16:38:40 UTC (49 KB) [v2] Wed, 26 Aug 2026 20:08:10 UTC (55 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.DG < prev | next > new | recent | 2025-09 Change to browse by: math math.AP math.PR 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) Major funding support from (opens in new tab) (opens in new tab) (opens in new tab)

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