Abstract / Synopsis
Too little mathematics has been written in prose. Thus we prove here, via a fantasy novellette, that a locally L-bilipschitz mapping f : X → Y between uniformly Ahlfors q-regular, complete and locally compact path-metric spaces X and Y is an L-bilipschitz map when Y is simply connected. The motivation for such a result arises from studying the asymptotic values of BLD-mappings with an empty branch set.
As far as the author is aware, the result is new, even though it would not be hard for specialists in the field to prove. The proof is essentially a modest extension of the ideas in [L17] in a more general setting when the branch set is empty.
Rami Luisto, "A Non-Euclidean Story or: How to Persist When Your Geometry Doesn’t," Journal of Humanistic Mathematics, Volume 12 Issue 1 (January 2022), pages 506-556. DOI: 10.5642/jhummath.202201.41. Available at: https://scholarship.claremont.edu/jhm/vol12/iss1/41