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It is proven that every fibred link in the 3-sphere S3 with k components can be obtained as the preimage of the braid axis for a d-sheeted simple branched cover over S3, branched along a suitable closed closed braid, with d=max{k,3}. More genera[...]texto impreso
Let U subset of R-d be open and convex. We prove that every (not necessarily Lipschitz or strongly) convex function f:U -> R can be approximated by real analytic convex functions, uniformly on all of U. We also show that C-0-fine approximation[...]texto impreso
Gallardo Gutiérrez, Eva A. ; González, M. J. ; Pérez González, Fernando ; Pommerenke, Christian ; Rattya, Jouni | Oxford University Press (OUP) | 2013-03We study geometric properties of the image of the unit circle under a bounded locally univalent function g such that log g' belongs either to the Dirichlet space D, VMOA or the little Bloch space B-0. Concerning VMOA and B-0, our findings genera[...]texto impreso
Recently, the author has given an alternate (and intrinsic) description of the shape category of metric compacta, based on the notion of multi-nets F:X?Y. These are defined as sequences (Fk) of upper semicontinuous multivalued mappings Fk:X?Y, w[...]texto impreso
Fernando Galván, José Francisco ; Gamboa, J. M. ; Ueno, Carlos | Oxford University Press (OUP) | 2011We show that convex polyhedra in R(n) and their interiors are images of regular maps R(n) -> R(n). As a main ingredient in the proof, given an n-dimensional, bounded, convex polyhedron K subset of R(n) and a point p is an element of R(n) \ K, w[...]texto impreso
Melle Hernández, Alejandro ; Fernández de Bobadilla de Olarzábal, Javier José ; Luengo Velasco, Ignacio ; Némethi , A. | Oxford University Press (OUP) | 2006-01In 2002, L. Nicolaescu and the fourth author formulated a very general conjecture which relates the geometric genus of a Gorenstein surface singularity with rational homology sphere link with the Seiberg--Witten invariant (or one of its candidat[...]texto impreso
Although the theory of singularities of curves - resolution, classification, numerical invariants - goes through with comparatively little change in finite characteristic, pencils of curves are more difficult. Bertini's theorem only holds in a m[...]texto impreso
Let C be a subset of ?n (not necessarily convex), f : C ? R be a function and G : C ? ?n be a uniformly continuous function, with modulus of continuity ?. We provide a necessary and sufficient condition on f, G for the existence of a convex func[...]
