1,721,084 research outputs found
Ritt's theorem and the Heins map in hyperbolic complex manifolds
No full textLet X be a Kobayashi hyperbolic complex manifold, and assume that X does not contain compact complex submanifolds of positive dimension (e.g., X Stein). We shall prove the following generalization of Ritt's theorem: every holomorphic self-map f:X -> X such that f (X) is relatively compact in X has a unique fixed point tau(f) is an element of X, which is attracting. Furthermore, we shall prove that tau(f) depends holomorphically on f in a suitable sense, generalizing results by Heins, Joseph-Kwack and the second author
Frames of quasi-geodesics, visibility, and geodesic loop
Full text linkIn this paper we give a characterization in terms of “quasi-geodesics frames’ of
visibility and existence of geodesic loops for bounded domains in C
d which are Kobayashi complete hyperbolic and Gromov hyperboli
Contact points and fractional singularities for semigroups of holomorphic self-maps of the unit disc
No full textWe study boundary singularities which can appear for infinitesimal generators of one-parameter semigroups of holomorphic self-maps of the unit disc. We introduce "regular" fractional singularities and characterize them in terms of the behavior of the associated semigroups and KA"nigs functions. We also provide necessary and sufficient geometric criteria on the shape of the image of the KA"nigs function for having such singularities. In order to do this, we study contact points of semigroups and prove that any contact (not fixed) point of a one-parameter semigroup corresponds to a maximal arc on the boundary to which the associated infinitesimal generator extends holomorphically as a vector field tangent to this arc
Residual indices of holomorphic maps relative to singular curves of fixed points on surfaces
No full textLet M be a two-dimensional complex manifold and let be a holomorphic map that fixes pointwise a (possibly) singular compact reduced and globally irreducible curve . We give a notion of degeneracy of f at a point of C. It turns out that f is non-degenerate at one point if and only if it is non-degenerate at every point of C. When f is non-degenerate on C we define a residual index for f at each point of C. Then we prove that the sum of the indices is equal to the self-intersection number of C. © Springer-Verlag Berlin Heidelberg 2002
Perturbation of baum-bott residues
No full textWe prove that Baum-Bott residues vary continuously in an appropriate sense under smooth deformations of holomorphic foliations. This provides an effective way of computing residues
Abel averages and holomorphically pseudo-contractive maps in Banach spaces
No full textA class of maps in a complex Banach space is studied, which includes both unbounded linear operators and nonlinear holomorphic maps. The defining property, which we call pseudo-contractivity, is introduced by means of the Abel averages of such maps. We show that the studied maps are dissipative in the spirit of the classical Lumer-Phillips theorem. For pseudo-contractive holomorphic maps, we establish the power convergence of the Abel averages to holomorphic retractions. (C) 2014 Elsevier Inc. All rights reserved
Index theorems for holomorphic self-maps
No full textWe prove several index theorems for holomorphic self-maps having positive-dimensional fixed points set. To do so we show that the fixed points set of a holomorphic self-map has a surprisingly rich structure, expressed by canonically defined meromorphic connections and bundle maps. Finally, we present some applications to holomorphic dynamics
Homeomorphic extension of quasi-isometries for convex domains in Cd and iteration theory
No full textEmbeddings of submanifolds and normal bundles
No full textThis paper studies the embeddings of a complex submanifold S inside a complex manifold M; in particular, we are interested in comparing the embedding of S in M with the embedding of S as the zero section in the total space of the normal bundle N(S) of S in M. We explicitly describe some cohomological classes allowing to measure the difference between the two embeddings, in the spirit of the work by Grauert, Griffiths, and Camacho, Movasati and Sad; we are also able to explain the geometrical meaning of the separate vanishing of these classes. Our results hold for any codimension, but even for curves in a surface we generalize previous results due to Laufert and Camacho, Movasati and Sad. (C) 2008 Elsevier Inc. All rights reserved
- …
