Peter Hasto -- A Proof of Hall's Conjecture on Length of Ray Images Under Starlike Mappings of Order alpha

Author information

• Peter Hasto
• University of Turku, Turku, Finland
• Website: https://www.problemsolving.fi/

Abstract:

In this talk, I will present results from an eponymous paper with S. Ponnusamy. Hall’s conjecture involves finding the exact constant for the generalization of the Gehring-Hayman theorem to starlike functions of order α>0. Our proof is in two parts: the reduction of the complex inequality to a family of real inequalities, and the solution of proof of these inequalities. After an overview of the conjecture’s history and a sketch of the first step I will mostly focus on the second step, with a particular emphasis on the rationale and process by which the proofs for the inequalities were generated.

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