Uniqueness of minimisers for a Grötzsch-Belinskiĭ type inequality in the Heisenberg group

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. Belinskiĭ studied these inequalities in the plane and identified the family of all minimisers. Beyond the Euclidean framework, a Grötzsch-Belinskiĭ-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.

Polnoe sobranie sochineniĭ /

Each vol. has also special t.p.

Bi͡elinskiĭ, ego zhizn' i perepiska.

Mode of access: Internet.

Demon--Angel--Rusalka--Son--Pi͡esni͡a pro Kalashnikova--Mt͡syri--Borodino--Skazka dli͡a di͡eteĭ--Duma--Proza--Portret--Bīografīi͡a--Bi͡elinskīĭ o poėzīi Lermontova.

Mode of access: Internet.

A.V. Kolʹt︠s︡ov kak poėt i chelovi︠e︡k; otzyvy V.G. Bi︠e︡linskago i Val. Maĭkova, pisʹma, "Zapisnai︠a︡ knizhka" i "Sobranīe poslovit︠s︡" Kolʹt︠s︡ova. S predisl. i primi︠e︡chanīi︠a︡mi sostaviteli︠a︡.

Mode of access: Internet.

V.G. Bi︠e︡linskīĭ. Ri︠e︡chʹ, proiznesennai︠a︡ vesnoi︠u︡ 1898 g. po sluchai︠u︡ 50-li︠e︡tīi︠a︡ so dni︠a︡ smerti Belinskago na russkikh sobranīi︠a︡kh v Zhenevi︠e︡, T︠S︡i︠u︡rikhi︠e︡ i Berni︠e︡.

Cover title.

V.G. Bi︠e︡linskīĭ : bīograficheskīĭ ocherk /

Mode of access: Internet.