A minimal area problem in conformal mapping

Dov Aharonov, Harold S. Shapiro, Alexander Yu Solynin

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Let S denote the usual class of functions f holomorphic and univalent in the unit disk U such that f(0) = f′(0) - 1 = 0. The main result of the paper is that area(f(U)) ≥ (27π/8)(2 - α)-2 for all f ∈ S such that |f″(0)| = 2α, 1/2 < α < 2. This solves a long-standing extremal problem for the class of functions considered.

Original languageEnglish
Pages (from-to)157-176
Number of pages20
JournalJournal d'Analyse Mathematique
StatePublished - 1999


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