Burger, M. Monod, N.
Published in
Journal of the European Mathematical Society

We prove that the natural map Hb2(Γ)?H2(Γ) from bounded to usual cohomology is injective if Γ is an irreducible cocompact lattice in a higher rank Lie group. This result holds also for nontrivial unitary coefficients, and implies finiteness results for Γ: the stable commutator length vanishes and any C1–action on the circle is almost trivial. We in...

Bertoin, Jean
Published in
Journal of the European Mathematical Society

The fragmentation processes considered in this work are self-similar Markov processes which are meant to describe the evolution of a mass that falls apart randomly as time passes. We investigate their pathwise asymptotic behavior as t→∞. In the so-called homogeneous case, we first point at a law of large numbers and a central limit theorem for (a m...

Pittet, Ch. Saloff-Coste, L.
Published in
Journal of the European Mathematical Society

We establish the lower bound p2t(e,e)≿exp(-t1/3), for the large times asymptotic behaviours of the probabilities p2t(e,e) of return to the origin at even times 2t, for random walks associated with finite symmetric generating sets of solvable groups of finite Prüfer rank. (A group has finite Prüfer rank if there is an integer r, such that any of its...

Cornea, Octav Ranicki, Andrew
Published in
Journal of the European Mathematical Society

We obtain rigidity and gluing results for the Morse complex of a real-valued Morse function as well as for the Novikov complex of a circle-valued Morse function. A rigidity result is also proved for the Floer complex of a hamiltonian defined on a closed symplectic manifold (M,ω) with c1|π2(M)=[ω]|π2(M)=0. The rigidity results for these complexes sh...

Alberti, G. Baldo, S. Orlandi, G.
Published in
Journal of the European Mathematical Society

The distributional k-dimensional Jacobian of a map u in the Sobolev space W1,k-1 which takes values in the the sphere Sk-1 can be viewed as the boundary of a rectifiable current of codimension k carried by (part of) the singularity of u which is topologically relevant. The main purpose of this paper is to investigate the range of the Jacobian opera...

Nabutovsky, Alexander Rotman, Regina
Published in
Journal of the European Mathematical Society

In this paper we present two upper bounds on the length of a shortest closed geodesic on compact Riemannian manifolds. The first upper bound depends on an upper bound on sectional curvature and an upper bound on the volume of the manifold. The second upper bound will be given in terms of a lower bound on sectional curvature, an upper bound on the d...

Loray, Frank Rebelo, Julio C.
Published in
Journal of the European Mathematical Society

We prove the existence of minimal and rigid singular holomorphic foliations by curves on the projective space ℂℙn for every dimension n≥2 and every degree d≥2. Precisely, we construct a foliation ℱ which is induced by a homogeneous vector field of degree d, has a finite singular set and all the regular leaves are dense in the whole of ℂℙn. Moreover...

De Lellis, Camillo Otto, Felix
Published in
Journal of the European Mathematical Society

In this paper, we establish rectifiability of the jump set of an S1–valued conservation law in two space–dimensions. This conservation law is a reformulation of the eikonal equation and is motivated by the singular limit of a class of variational problems. The only assumption on the weak solutions is that the entropy productions are (signed) Radon ...

Koskela, Pekka Malý, Jan
Published in
Journal of the European Mathematical Society

Wang, Wei
Published in
Journal of the European Mathematical Society

We construct the CR invariant canonical contact form can(J) on scalar positive spherical CR manifold (M,J), which is the CR analogue of canonical metric on locally conformally flat manifold constructed by Habermann and Jost. We also construct another canonical contact form on the Kleinian manifold Ω(Γ)/Γ, where Γ is a convex cocompact subgroup of A...