Compact harmonic RCD$(K, N)$ spaces are harmonic manifolds

[2412.20841] Compact harmonic RCD$(K, N)$ spaces are harmonic manifolds Skip to main content Search Submit Donate Log in Mathematics > Differential Geometry arXiv:2412.20841 (math) [Submitted on 30 Dec 2024 ( v1 ), last revised 12 Oct 2025 (this version, v2)] Title: Compact harmonic RCD$(K, N)$ spaces are harmonic manifolds Authors: Zhangkai Huang View PDF HTML (experimental) Abstract: In this paper, we study harmonic RCD$(K,N)$ spaces as the counterpart of harmonic Riemannian manifolds with Ricci curvature bounded from below. We prove that a compact RCD$(K,N)$ space is isometric to a smooth closed Riemannian manifold if it satisfies either of the following harmonicity conditions:(1) the heat kernel $\rho(x,y,t)$ depends only on the variable $t$ and the distance between points $x$ and $y$; (2) the volume of the intersection of two geodesic balls depends only on their radii and the distance between their centers. Subjects: Differential Geometry (math.DG) ; Metric Geometry (math.MG) MSC classes: 28A75 Cite as: arXiv:2412.20841 [math.DG] (or arXiv:2412.20841v2 [math.DG] for this version) https://doi.org/10.48550/arXiv.2412.20841 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Nonlinear Anal. TMA 274 (2027) 114269 Related DOI : https://doi.org/10.1016/j.na.2026.114269 Focus to learn more DOI(s) linking to related resources Submission history From: Zhangkai Huang [ view email ] [v1] Mon, 30 Dec 2024 10:16:11 UTC (41 KB) [v2] Sun, 12 Oct 2025 14:24:26 UTC (48 KB) Full-text links: Access Paper: 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.MG 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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