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arXiv · 2604.03036

A note on the Erd\"os minimal area problem

Subhajit Ghosh·Koushik Ramachandran
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Abstract

We answer a question of Erd\H{o}s, 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.

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Subhajit Ghosh, Koushik Ramachandran. 2026-04-03. A note on the Erd\"os minimal area problem. https://doi.org/10.1090/proc/17897

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