77,334 research outputs found
A diagrammatic approach to categorification of quantum groups III
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
©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
We construct a family of homeomorphisms of the
two-torus isotopic to the identity, for which all of the rotation sets
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 , 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 varies continuously with
, the set of extreme points of 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
We prove that any weakly acausal curve in the boundary of Anti-de
Sitter (2+1)-space is the asymptotic boundary of two spacelike -surfaces,
one of which is past-convex and the other future-convex, for every
. The curve is the graph of a quasisymmetric
homeomorphism of the circle if and only if the -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
, every quasisymmetric homeomorphism of the circle admits a
unique extension which is a -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
We study a simple problem that arises from the study of Lorentz surfaces and
Anosov flows. For a non decreasing map of degree one , we are interested in groups of circle diffeomorphisms that act
on the complement of the graph of in by
preserving a volume form. We show that such groups are semi conjugate to
subgroups of , and that when , we have a topological conjugacy. We also
construct examples, where is not continuous, for which there is no such
conjugacy.Comment: 27 pages, 7 figures. arXiv admin note: text overlap with
arXiv:1402.042
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