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

Balogh, Zoltan; Fässler, Katrin; Platis, Ioannis (2015). Uniqueness of minimisers for a Grötzsch-Belinskiĭ type inequality in the Heisenberg group. Conformal geometry and dynamics, 19(6), pp. 122-145. American Mathematical Society 10.1090/ecgd/278

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First published in Conform. Geom. Dyn. 19 (2015), 122-145 , published by the American Mathematical Society

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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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Balogh, Zoltan; Fässler, Katrin and Platis, Ioannis

Subjects:

500 Science > 510 Mathematics

ISSN:

1088-4173

Publisher:

American Mathematical Society

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

08 Jun 2016 16:11

Last Modified:

02 Aug 2017 15:41

Publisher DOI:

10.1090/ecgd/278

BORIS DOI:

10.7892/boris.81136

URI:

https://boris.unibe.ch/id/eprint/81136

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