In: Mathematische Zeitschrift, 2015, vol. 281, no. 1-2, p. 379-393
|
In: Geometriae Dedicata, 2015, vol. 175, no. 1, p. 281-307
|
In: International Mathematics Research Notices, 2017, vol. 2017, no. 8, p. 2367-2401
|
In: Calculus of Variations and Partial Differential Equations, 2020, vol. 59, no. 5, p. 177
We find maximal representatives within equivalence classes of metric spheres. For Ahlfors regular spheres these are uniquely characterized by satisfying the seemingly unrelated notions of Sobolev-to-Lipschitz property, or volume rigidity. We also apply our construction to solutions of the Plateau problem in metric spaces and obtain a variant of the associated intrinsic disc studied by...
|
In: Geometriae Dedicata, 2020, vol. 206, no. 1, p. 151–179
Let Sg,n be a surface of genus g>1 with n>0 punctures equipped with a complete hyperbolic cusp metric. Then it can be uniquely realized as the boundary metric of an ideal Fuchsian polyhedron. In the present paper we give a new variational proof of this result. We also give an alternative proof of the existence and uniqueness of a hyperbolic polyhedral metric with prescribed curvature in a...
|
In: Inventiones mathematicae, 2014, vol. 197, no. 3, p. 663-682
|
In: Zeitschrift für Physikalische Chemie, 2015, vol. 229, no. 10-12, p. 1475-1501
|
In: Advances in Mathematics, 2019, vol. 343, p. 910–934
|
In: Discrete Mathematics, 2018, vol. 341, no. 11, p. 3123–3133
The chromatic number of a subset of Euclidean space is the minimal number of colors sufficient for coloring all points of this subset in such a way that any two points at the distance 1 have different colors. We give new upper bounds on chromatic numbers of spheres. This also allows us to give new upper bounds on chromatic numbers of any bounded subsets.
|
In: Physical Review E, 2018, vol. 97, no. 4, p. 040601
We explore the glassy dynamics of soft colloids using microgels and charged particles interacting by steric and screened Coulomb interactions, respectively. In the supercooled regime, the structural relaxation time τα of both systems grows steeply with volume fraction, reminiscent of the behavior of colloidal hard spheres. Computer simulations confirm that the growth of τα on approaching...
|