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.
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)
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