For bounded convex domains, equality holds in the extremal problem for harmonic maps conformal at a point if and only if the domain is the image of the unit disc under a holomorphic map with derivative of the form c/(1 + a z + λ z²) satisfying the given bounds on a and λ.
Darboux, De l’emploi des fonctions elliptiques dans l’th´ eorie du qu adrilatere plan , Bulletin des Sciences Math´ ematiques et Astronomiques3 (1879), 109–120
2 Pith papers cite this work. Polarity classification is still indexing.
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Explicit necessary and sufficient conditions are derived for finite groups of order 2n in quarter-plane random walks and for n-periodic Darboux transformations of 4-bar links, for every n greater than or equal to 2.
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On an extremal problem for harmonic maps conformal at a point
For bounded convex domains, equality holds in the extremal problem for harmonic maps conformal at a point if and only if the domain is the image of the unit disc under a holomorphic map with derivative of the form c/(1 + a z + λ z²) satisfying the given bounds on a and λ.
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Finite Groups of Random Walks in the Quarter Plane and Periodic $4$-bar Links
Explicit necessary and sufficient conditions are derived for finite groups of order 2n in quarter-plane random walks and for n-periodic Darboux transformations of 4-bar links, for every n greater than or equal to 2.