The Kähler-Ricci soliton on bounded pseudoconvex domains

[2412.03345] The Kähler-Ricci soliton on bounded pseudoconvex domains Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Complex Variables arXiv:2412.03345 (math) [Submitted on 4 Dec 2024 ( v1 ), last revised 14 Apr 2026 (this version, v4)] Title: The Kähler-Ricci soliton on bounded pseudoconvex domains Authors: Zehao Sha View a PDF of the paper titled The K\"ahler-Ricci soliton on bounded pseudoconvex domains, by Zehao Sha View PDF HTML (experimental) Abstract: In this paper, we study Kähler-Ricci solitons on bounded pseudoconvex domains in $\mathbb{C}^n$ with $C^2$ boundary. Under suitable assumptions, we prove that such solitons must be Kähler-Einstein. Building on Huang and Xiao's resolution of Cheng's conjecture, we further establish an analogous result for Bergman Kähler-Ricci solitons. Several model domains are presented to illustrate our results. Comments: 19 pages. More details added Subjects: Complex Variables (math.CV) ; Differential Geometry (math.DG) MSC classes: 53C55, 32Q02 Cite as: arXiv:2412.03345 [math.CV] (or arXiv:2412.03345v4 [math.CV] for this version) https://doi.org/10.48550/arXiv.2412.03345 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Zehao Sha [ view email ] [v1] Wed, 4 Dec 2024 14:26:15 UTC (16 KB) [v2] Thu, 5 Dec 2024 15:54:01 UTC (1 KB) (withdrawn) [v3] Thu, 9 Jan 2025 22:35:55 UTC (17 KB) [v4] Tue, 14 Apr 2026 08:11:30 UTC (20 KB) Full-text links: Access Paper: View a PDF of the paper titled The K\"ahler-Ricci soliton on bounded pseudoconvex domains, by Zehao Sha View PDF HTML (experimental) TeX Source view license Current browse context: math.CV < prev | next > new | recent | 2024-12 Change to browse by: math math.DG 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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