Serrin's overdetermined problem implies the domain is a disk among rectifiable Jordan Smirnov domains, but non-disk rectifiable non-Smirnov Jordan domains exist that satisfy the equivalent harmonic quadrature identity.
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Serrin's overdetermined problem and sharp harmonic quadrature identities in the plane
Serrin's overdetermined problem implies the domain is a disk among rectifiable Jordan Smirnov domains, but non-disk rectifiable non-Smirnov Jordan domains exist that satisfy the equivalent harmonic quadrature identity.