Related papers: Geometric Rigidity Estimates for Incompatible Fiel…

We give a geometric characterization of the quantitative non-integrability, introduced by Katz, of strong stable and unstable bundles of partially hyperbolic measures and sets in dimension 3. This is done via the use of higher order…

Let $M$ be a closed complex submanifold in ${\mathbb C}^N$ with the complete K\"ahler metric induced by the Euclidean metric. Several finiteness theorems on the $L^p$ Bergman space of holomorphic sections of a given Hermitian line bundle…

Homogenization of a spectral problem in a bounded domain with a high contrast in both stiffness and density is considered. For a special critical scaling, two-scale asymptotic expansions for eigenvalues and eigenfunctions are constructed.…

This is the final part of a series of papers where we study perturbations of divergence form second order elliptic operators $-\operatorname{div} A \nabla$ by first and zero order terms, whose complex coefficients lie in critical spaces,…

For $2\leq p\leq \infty$, we establish dimension-free estimates for discrete dyadic Hardy-Littlewood maximal operators over Euclidean balls on semi-commutative $L_{p}$ space. In particular, when the radius is sufficiently large, these…

We use ideas on integrability in higher dimensions to define Lorentz invariant field theories with an infinite number of local conserved currents. The models considered have a two dimensional target space. Requiring the existence of…

In the paper [L. Fei et al., JHEP 09 (2015) 076] a cubic field theory of a scalar field $\sigma$ and two anticommuting scalar fields, $\theta$ and $\bar \theta$, was formulated. In $6-\epsilon$ dimensions it has a weakly coupled fixed point…

The behavior of many critical phenomena at large distances is expected to be invariant under the full conformal group, rather than only isometries and scale transformations. When studying critical phenomena, approximations are often…

We show with two numerical examples that the conventional expansion in powers of the field for the critical potential of 3-dimensional O(N) models in the large-N limit, does not converge for values of phi^2 larger than some critical value.…

We consider a $\varphi$-rigidity property for divergence-free vector fields in the Euclidean $n$-space, where $\varphi(t)$ is a non-negative convex function vanishing only at $t=0$. We show that this property is always satisfied in…

Direct verification of the existence of an infinite set of multicritical non-perturbative FPs (Fixed Points) for a single scalar field in two dimensions, is in practice well outside the capabilities of the present standard approximate…

We show that singular sets of free boundaries arising in codimension one anisotropic geometric variational problems are $\mathcal H ^{n-3}$-negligible, where $n$ is the ambient space dimension. In particular our results apply to capillarity…

An important unanswered question in quantum field theory is to understand precisely under which conditions scale invariance implies invariance under the full conformal group. While the general answer in two dimensions has been known for…

In projective dimension growth results, one bounds the number of rational points of height at most $H$ on an irreducible hypersurface in $\mathbb P^n$ of degree $d>3$ by $C(n)d^2 H^{n-1}(\log H)^{M(n)}$, where the quadratic dependence in…

The restriction problem is better understood for hypersurfaces and recent progresses have been made by bilinear and multilinear approaches and most recently polynomial partitioning method which is combined with those estimates. However, for…

For disordered elastic manifolds in the ground state (equilibrium) we obtain the critical exponents for the roughness and the correction-to-scaling up to 3-loop order, i.e. third order in $\epsilon=4-d$, where $d$ is the internal dimension…

It is shown by a counterexample that isocapacitary and isoperimetric constants of a multi-dimensional Euclidean domain starshaped with respect to a ball are not equivalent. Sharp integral inequalities involving the harmonic capacity which…

We find necessary and sufficient conditions for the validity of weighted Rellich and Calderon-Zygmund inequalities in L^p, 1 \leq p \leq \infty, in the whole space and in the half-space with Dirichlet boundary conditions. General operators…

We study the critical behaviour of spherically symmetric scalar field collapse to black holes in spacetime dimensions other than four. We obtain reliable values for the scaling exponent in the supercritical region for dimensions in the…

In this article we obtain $L^2$ bounds for strongly singular integrals along curves in $\R^d;$ our results both generalise and extend to higher dimensions those obtained by Chandarana in the plane. Moreover, we show that the operators in…