A sharp inequality for harmonic diffeomorphisms of the unit disk
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🧮 math.CV
keywords
diskharmonicunitdiffeomorphismsdomaininequalitybeltramicase
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We extend the classical Schwarz-Pick inequality to the class of harmonic mappings between the unit disk and a Jordan domain with given perimeter. It is intriguing that the extremals in this case are certain harmonic diffeomorphisms between the unit disk and a convex domain that solve the Beltrami equation of second order.
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