Uniqueness of Minimisers for a Grötzsch-belinskĭi Type Inequality in the Heisenberg Group
نویسندگان
چکیده
The modulus method introduced by H. Grötzsch yields bounds for a mean distortion functional of quasiconformal maps between two annuli mapping the respective boundary components onto each other. P. P. Belinskĭı studied these inequalities in the plane and identified the family of all minimisers. Beyond the Euclidean framework, a Grötzsch–Belinskĭı-type inequality has been previously considered for quasiconformal maps between annuli in the Heisenberg group whose boundaries are Korányi spheres. In this note we show that—in contrast to the planar situation—the minimiser in this setting is essentially unique.
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