We prove that a wide range of coloring problems for graphs on surfaces can be resolved by inspecting finite number configurations.

We investigate the fate of determinism in general relativity (GR), comparing philosopher’s account with physicist’s well-posed initial value formulations. The is interwoven question what it for a spacetime to be ‘physically reasonable’. A central concern status global hyperbolicity, putatively necessary condition GR. While hyperbolicity may fail true all physically reasonable models, we analyze...

We introduce a new hyperbolicity condition for set-valued dynamical systems and show that this condition implies the shadowing and inverse shadowing properties.

We study in this paper quasiperiodic maximal surfaces pseudo-hyperbolic spaces and show that they are characterised by a curvature condition, Gromov hyperbolicity or conformal hyperbolicity. the limit curves of these Einstein Universe admits canonical quasisymmetric parametrisation, while conversely every curve bounds surface such way parametrisation is continuous extension uniformisation; we g...

Using degeneration to scrolls, we give an easy proof of non–existence of curves of low genera on general surfaces in P of degree d ≥ 5. We show, along the same lines, boundedness of families of curves of small enough genera on general surfaces in P. We also show that there exist Kobayashi hyperbolic surfaces in P of degree d = 7 (a result so far unknown), and give a new construction of such sur...

We study complex hyperbolicity in the setting of geometric orbifolds introduced by F. Campana. Generalizing classical methods to this context, we obtain degeneracy statements for entire curves with ramification in situations where no Second Main Theorem is known from value distribution theory.

The usual deenition of hyperbolicity of a group G demands that all geodesic triangles in the Cayley graph of G should be thin. Using the theorem that a subquadratic isoperimetric inequality implies a linear one, we show that it is in fact only necessary for all triangles from a given combing to be thin, thus giving a new criterion for hyperbolicity of nitely presented groups. Given a group G th...