3 papers
math.DG2025
A discrete version of Liouville's theorem on conformal maps
Ulrich Pinkall, Boris Springborn
Liouville's theorem says that in dimension greater than two, all conformal maps are Möbius transformations. We prove an analogous statement about simplicial complexes, where two s…
math.MG2025
Ideal hyperbolic polyhedra and discrete uniformization
Boris Springborn
We provide a constructive, variational proof of Rivin's realization theorem for ideal hyperbolic polyhedra with prescribed intrinsic metric, which is equivalent to a discrete unifo…
math.NT2024
The worst approximable rational numbers
Boris Springborn
We classify and enumerate all rational numbers with approximation constant at least using hyperbolic geometry. Rational numbers correspond to geodesics in the modular…