Mucci, Domenico
Published in
Journal of the European Mathematical Society

For vector valued maps, convergence in W1,1 and of all minors of the Jacobian matrix in L1 is equivalent to convergence weakly in the sense of currents and in area for graphs. We show that maps defined on domains of dimension n≥ 3 can be approximated strongly in this sense by smooth maps if and only if the same property holds for the restriction to...

Harris, M. Scholl, A.J.
Published in
Journal of the European Mathematical Society

We extend Prasad’s results on the existence of trilinear forms on representations of GL2 of a local field, by permitting one or more of the representations to be reducible principal series, with infinite-dimensional irreducible quotient. We apply this in a global setting to compute (unconditionally) the dimensions of the subspaces of motivic cohomo...

Ambrosio, Luigi Caselles, Vicent Masnou, Simon Morel, Jean-Michel
Published in
Journal of the European Mathematical Society

This paper contains a systematic analysis of a natural measure theoretic notion of connectedness for sets of finite perimeter in ℝN, introduced by H. Federer in the more general framework of the theory of currents. We provide a new and simpler proof of the existence and uniqueness of the decomposition into the so-called M-connected components. More...

Lawler, Gregory F. Werner, Wendelin
Published in
Journal of the European Mathematical Society

We construct a class of conformally invariant measures on sets (or paths) and we study the critical exponents called intersection exponents associated to these measures. We show that these exponents exist and that they correspond to intersection exponents between planar Brownian motions. More precisely, using the definitions and results of our pape...

Struwe, Michael
Published in
Journal of the European Mathematical Society

For semilinear elliptic equations of critical exponential growth we establish the existence of positive solutions to the Dirichlet problem on suitable non-contractible domains.

Lindenstrauss, J. Preiss, D.
Published in
Journal of the European Mathematical Society

We give a relatively simple (self-contained) proof that every real-valued Lipschitz function on ℓ2 (or more generally on an Asplund space) has points of Fréchet differentiability. Somewhat more generally, we show that a real-valued Lipschitz function on a separable Banach space has points of Fréchet differentiability provided that the w* closure of...

van der Geer, G. Katsura, T.
Published in
Journal of the European Mathematical Society

In this paper we give a characterization of the height of K3 surfaces in characteristic p>0. This enables us to calculate the cycle classes in families of K3 surfaces of the loci where the height is at least h. The formulas for such loci can be seen as generalizations of the famous formula of Deuring for the number of supersingular elliptic curves ...

Filo, Ján Luckhaus, Stephan
Published in
Journal of the European Mathematical Society

An asymptotic analysis is given for the heat equation with mixed boundary conditions rapidly oscillating between Dirichlet and Neumann type. We try to present a general framework where deterministic homogenization methods can be applied to calculate the second term in the asymptotic expansion with respect to the small parameter characterizing the o...

Kahn, Bruno Sujatha, R.
Published in
Journal of the European Mathematical Society

This is the last of a series of three papers where we compute the unramified cohomology of quadrics in degree up to 4. Complete results were obtained in the two previous papers for quadrics of dimension ≤4 and ≥11. Here we deal with the remaining dimensions between 5 and 10. We also prove that the unramified cohomology of Pfister quadrics with divi...

Sznitman, Alain-Sol
Published in
Journal of the European Mathematical Society

This work is concerned with asymptotic properties of multi-dimensional random walks in random environment. Under Kalikow’s condition, we show a central limit theorem for random walks in random environment on ℤd, when d≥2. We also derive tail estimates on the probability of slowdowns. These latter estimates are of special interest due to the natural...