A remark on quasiconformal mappings on Carnot groups.
Copyright policy )A remark on quasiconformal mappings on Carnot groups.
A. Koranyi and M. Reimann informed me that a result of theirs on the theory of quasiconformal mappings on the Heisenberg groups contradicted inequality (20.17) in my monograph [Strong rigidity of locally symmetric spaces, Ann. Math. Studies, No. 78 (Princeton 1973; Zbl 0265.53039)] which is asserted there without proof and used in the proof of Proposition 21.3. Proposition 21.3 is an essential step in proving strong rigidity for locally hyperbolic spaces. This paper offers a correction of the proof of Proposition 21.3 via bypassing the faulty inequality (20.17). The method used can be generalized directly to simplify the definition of quasiconformal mappings on two-step Carnot groups.
quasiconformal mappings, Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations, Heisenberg groups, 53C20, Discrete subgroups of Lie groups, two-step Carnot groups, 22E40, Global Riemannian geometry, including pinching, strong rigidity, locally hyperbolic spaces
quasiconformal mappings, Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations, Heisenberg groups, 53C20, Discrete subgroups of Lie groups, two-step Carnot groups, 22E40, Global Riemannian geometry, including pinching, strong rigidity, locally hyperbolic spaces
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