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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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) |
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Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |
UniBE Contributor: |
Balogh, Zoltan, Fässler, Katrin, 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: |
05 Dec 2022 14:55 |
Publisher DOI: |
10.1090/ecgd/278 |
BORIS DOI: |
10.7892/boris.81136 |
URI: |
https://boris.unibe.ch/id/eprint/81136 |