A note on the Erdös minimal area problem

[2604.03036] A note on the Erdös minimal area problem Skip to main content Search Submit Donate Log in Mathematics > Complex Variables arXiv:2604.03036 (math) [Submitted on 3 Apr 2026 ( v1 ), last revised 27 Aug 2026 (this version, v3)] Title: A note on the Erdös minimal area problem Authors: Subhajit Ghosh , Koushik Ramachandran View PDF HTML (experimental) Abstract: We answer a question of Erdős, Herzog, and Piranian \cite[Problem $4$, page $135$]{EHP} on the minimal area of polynomial lemniscates when all the zeros of the polynomial are constrained to lie on a compact set $K$ whose logarithmic capacity is greater than $1$. We show that the minimal area decays exponentially fast and prove that the Fekete polynomials are asymptotic minimizers for the area problem. Comments: 14 pages, corrected some typos. Some new results added. Accepted for publication in the Proceedings of the AMS, Subjects: Complex Variables (math.CV) ; Classical Analysis and ODEs (math.CA); Metric Geometry (math.MG) MSC classes: 30C10, 31A15 Cite as: arXiv:2604.03036 [math.CV] (or arXiv:2604.03036v3 [math.CV] for this version) https://doi.org/10.48550/arXiv.2604.03036 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1090/proc/17897 Focus to learn more DOI(s) linking to related resources Submission history From: Subhajit Ghosh [ view email ] [v1] Fri, 3 Apr 2026 13:45:51 UTC (8 KB) [v2] Wed, 27 May 2026 11:40:15 UTC (12 KB) [v3] Thu, 27 Aug 2026 06:54:20 UTC (135 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.CV < prev | next > new | recent | 2026-04 Change to browse by: math math.CA 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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