Zobrazeno 1 - 10
of 78
pro vyhledávání: '"Springborn, Boris"'
Autor:
Springborn, Boris
Publikováno v:
J. Number Theory, 263:153--205, 2024
We classify and enumerate all rational numbers with approximation constant at least $\frac{1}{3}$ using hyperbolic geometry. Rational numbers correspond to geodesics in the modular torus with both ends in the cusp, and the approximation constant meas
Externí odkaz:
http://arxiv.org/abs/2209.15542
Autor:
Pinkall, Ulrich, Springborn, Boris
Liouville's theorem says that in dimension greater than two, all conformal maps are M\"obius transformations. We prove an analogous statement about simplicial complexes, where two simplicial complexes are considered discretely conformally equivalent
Externí odkaz:
http://arxiv.org/abs/1911.00966
A famous construction of Gelfand, Kapranov and Zelevinsky associates to each finite point configuration $A \subset \mathbb{R}^d$ a polyhedral fan, which stratifies the space of weight vectors by the combinatorial types of regular subdivisions of $A$.
Externí odkaz:
http://arxiv.org/abs/1708.08714
Autor:
Springborn, Boris
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 uniformization theorem for spheres. The same variational method is also use
Externí odkaz:
http://arxiv.org/abs/1707.06848
Autor:
Springborn, Boris
Publikováno v:
Enseign. Math. 63 (2017), no. 3-4, 333-373
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 farthest away from zero. The main purpose of this paper is to present a
Externí odkaz:
http://arxiv.org/abs/1702.05061
Publikováno v:
A. I. Bobenko (editor). Advances in Discrete Differential Geometry, Springer, Berlin, 2016, pages 177-195. (Open access)
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 principle involving the central angles of the polygon as variables. The un
Externí odkaz:
http://arxiv.org/abs/1506.08069
Publikováno v:
Discrete Comput. Geom. 57:2 (2017), 305-317
We consider the quasiconformal dilatation of projective transformations of the real projective plane. For non-affine transformations, the contour lines of dilatation form a hyperbolic pencil of circles, and these are the only circles that are mapped
Externí odkaz:
http://arxiv.org/abs/1505.01341
Berlin, Techn. Univ., Diss., 2003.
Computerdatei im Fernzugriff.
Computerdatei im Fernzugriff.
Publikováno v:
Geom. Dedicata 166:1 (2013), 15-29
There is no 5,7-triangulation of the torus, that is, no triangulation with exactly two exceptional vertices, of degree 5 and 7. Similarly, there is no 3,5-quadrangulation. The vertices of a 2,4-hexangulation of the torus cannot be bicolored. Similar
Externí odkaz:
http://arxiv.org/abs/1207.3605