227 citations · 473 across the 16 of their papers we have counts for
16 papers
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…
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 si…
Secondary fans and secondary polyhedra of punctured Riemann surfaces
Michael Joswig, Robert Löwe, Boris Springborn
A famous construction of Gelfand, Kapranov and Zelevinsky associates to each finite point configuration a polyhedral fan, which stratifies the space of wei…
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…
The hyperbolic geometry of Markov's theorem on Diophantine approximation and quadratic forms
Boris Springborn
Markov's theorem classifies the worst irrational numbers with respect to rational approximation and the indefinite binary quadratic forms whose values for integer arguments stay fa…
A variational principle for cyclic polygons with prescribed edge lengths
Hana Kouřimská, Lara Skuppin, Boris Springborn
We provide a new proof of the elementary geometric theorem on the existence and uniqueness of cyclic polygons with prescribed side lengths. The proof is based on a variational prin…