Moebius transformations preserving fixed anharmonic ratio
Vladislav Aseev, Tatyana Kergylova
TL;DR
This paper extends Kobayashi's 2007 result by showing that Moebius transformations can be characterized as mappings preserving anharmonic ratio without needing differentiability or injectivity.
Contribution
The paper proves that the preservation of anharmonic ratio alone suffices to identify Moebius transformations, removing the assumptions of differentiability and injectivity.
Findings
Moebius transformations characterized by anharmonic ratio preservation
No need for differentiability or injectivity in the characterization
Strengthens previous results by Kobayashi (2007)
Abstract
O. Kobayashi in 2007 proved that differentiable mappings preserving anharmonic ratio are Moebius transformations. We strengthen his result and prove, that the requirement of differentiability and even of injectivity can be omitted.
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Taxonomy
TopicsAnalytic and geometric function theory · Mathematics and Applications · Algebraic and Geometric Analysis