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Ideal bicombings for hyperbolic groups and applications

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Harmonic Active Contours

Jean-Philippe Thiran, Xavier Bresson, Dominique Zosso, Virginia Estellers Casas

We propose a segmentation method based on the geometric representation of images as two-dimensional manifolds embedded in a higher dimensional space. The segmentation is formulated as a minimization problem, where the contours are described by a level set ...

Institute of Electrical and Electronics Engineers2014

On some convex cocompact groups in real hyperbolic space

Marc Desgroseilliers

We generalize to a wider class of hyperbolic groups a construction by Misha Kapovich yielding convex cocompact representations into real hyperbolic space. ...

Geometry & Topology Publications2013

The Energy Density in the Planar Ising Model

Clément Hongler, Stanislav Smirnov

We study the critical Ising model on the square lattice in bounded simply connected domains with + and free boundary conditions. We relate the energy density of the model to a discrete fermionic spinor and compute its scaling limit by discrete complex anal ...

2013

Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. II

Martins Bruveris, Martin Bauer

The geodesic distance vanishes on the group of compactly supported diffeomorphisms of a Riemannian manifold of bounded geometry, for the right invariant weak Riemannian metric which is induced by the Sobolev metric of order on the Lie algebra of vector fie ...

Springer Verlag2013

Fixed Point Property For Universal Lattice On Schatten Classes

Masato Mimura

The special linear group G = SLn(Z[x(1), ... , x(k)]) (n at least 3 and k finite) is called the universal lattice. Let n be at least 4, and p be any real number in (1, infinity). The main result is the following: any finite index subgroup of G has the fixe ...

Amer Mathematical Soc2013

Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group

Martins Bruveris, Martin Bauer

We study Sobolev-type metrics of fractional order s a parts per thousand yen 0 on the group Diff (c) (M) of compactly supported diffeomorphisms of a manifold M. We show that for the important special case M = S (1), the geodesic distance on Diff (c) (S (1) ...

Springer Verlag2013

Closing Large Hyperbolic 2g-gons

Poincaré's uniformisation theorem says that any Riemann surface is conformally equivalent to a unique (up to isometry) surface of constant Gauss curvature 0, 1 or –1. The (topologically) richest of these three worlds is for curvature –1 formed of hyperboli ...

EPFL2012

Finite Element Method on Riemann Surfaces and Applications to the Laplacian Spectrum

Marc Maintrot

The objective of this PhD thesis is the approximate computation of the solutions of the Spectral Problem associated with the Laplace operator on a compact Riemann surface without boundaries. A Riemann surface can be seen as a gluing of portions of the Hype ...

EPFL2012

Lambert cubes and the Lobell polyhedron revisited

The first example of a closed orientable hyperbolic 3-manifold was constructed by F. Lobell in 1931 from eight copies of the right-angled 14-hedron. We consider the family of hyperbolic polyhedra which generalize the Lambert cube and the Lobell polyhedron. ...

Walter De Gruyter & Co2012

Concentration Compactness for critical wave maps

Joachim Krieger

Wave maps are the simplest wave equations taking their values in a Riemannian manifold (M,g). Their Lagrangian is the same as for the scalar equation, the only difference being that lengths are measured with respect to the metric g. By Noether's theorem, s ...

European Mathematical Society2012