77,334 research outputs found

    A diagrammatic approach to categorification of quantum groups III

    Full text link
    We categorify the idempotented form of quantum sl(n).Comment: 88 pages, LaTeX2e with xypic and pstricks macros, 3 eps file

    An Image Morphing Technique Based on Optimal Mass Preserving Mapping

    Get PDF
    ©2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.DOI: 10.1109/TIP.2007.896637Image morphing, or image interpolation in the time domain, deals with the metamorphosis of one image into another. In this paper, a new class of image morphing algorithms is proposed based on the theory of optimal mass transport. The 2 mass moving energy functional is modified by adding an intensity penalizing term, in order to reduce the undesired double exposure effect. It is an intensity-based approach and, thus, is parameter free. The optimal warping function is computed using an iterative gradient descent approach. This proposed morphing method is also extended to doubly connected domains using a harmonic parameterization technique, along with finite-element methods

    New Rotation Sets in a Family of Torus Homeomorphisms

    Get PDF
    We construct a family {Φt}t[0,1]\{\Phi_t\}_{t\in[0,1]} of homeomorphisms of the two-torus isotopic to the identity, for which all of the rotation sets ρ(Φt)\rho(\Phi_t) can be described explicitly. We analyze the bifurcations and typical behavior of rotation sets in the family, providing insight into the general questions of toral rotation set bifurcations and prevalence. We show that there is a full measure subset of [0,1][0,1], consisting of infinitely many mutually disjoint non-trivial closed intervals, on each of which the rotation set mode locks to a constant polygon with rational vertices; that the generic rotation set in the Hausdorff topology has infinitely many extreme points, accumulating on a single totally irrational extreme point at which there is a unique supporting line; and that, although ρ(t)\rho(t) varies continuously with tt, the set of extreme points of ρ(t)\rho(t) does not. The family also provides examples of rotation sets for which an extreme point is not represented by any minimal invariant set, or by any directional ergodic measure.Comment: Author's accepted version. The final publication is available at Springer via http://dx.doi.org/10.1007/s00222-015-0628-

    Area-preserving diffeomorphism of the hyperbolic plane and K-surfaces in Anti-de Sitter space

    Full text link
    We prove that any weakly acausal curve Γ\Gamma in the boundary of Anti-de Sitter (2+1)-space is the asymptotic boundary of two spacelike KK-surfaces, one of which is past-convex and the other future-convex, for every K(,1)K\in(-\infty,-1). The curve Γ\Gamma is the graph of a quasisymmetric homeomorphism of the circle if and only if the KK-surfaces have bounded principal curvatures. Moreover in this case a uniqueness result holds. The proofs rely on a well-known correspondence between spacelike surfaces in Anti-de Sitter space and area-preserving diffeomorphisms of the hyperbolic plane. In fact, an important ingredient is a representation formula, which reconstructs a spacelike surface from the associated area-preserving diffeomorphism. Using this correspondence we then deduce that, for any fixed θ(0,π)\theta\in(0,\pi), every quasisymmetric homeomorphism of the circle admits a unique extension which is a θ\theta-landslide of the hyperbolic plane. These extensions are quasiconformal.Comment: 47 pages, 18 figures. More details added to Remark 4.14, Remark 6.2 and Theorem 7.8 Step 2. Several references added and typos corrected. Final version. To appear in Journal of Topolog

    Convergence groups and semi conjugacy

    Full text link
    We study a simple problem that arises from the study of Lorentz surfaces and Anosov flows. For a non decreasing map of degree one h:S1S1h:\mathbb{S}^1\to \mathbb{S}^1, we are interested in groups of circle diffeomorphisms that act on the complement of the graph of hh in S1×S1\mathbb{S}^1\times \mathbb{S}^1 by preserving a volume form. We show that such groups are semi conjugate to subgroups of PSL(2,R)\mathrm{PSL}(2,\mathbb{R}), and that when hHomeo(S1)h\in \mathrm{Homeo}(\mathbb{S}^1), we have a topological conjugacy. We also construct examples, where hh is not continuous, for which there is no such conjugacy.Comment: 27 pages, 7 figures. arXiv admin note: text overlap with arXiv:1402.042
    corecore