Related papers: Uniform concentration property for Griffith almost…

We solve explicitly a certain minimization problem for probability measures involving an interaction energy that is repulsive at short distances and attractive at large distances. We complement earlier works by showing that part of the…

We prove higher order concentration bounds for functions on Stiefel and Grassmann manifolds equipped with the uniform distribution. This partially extends previous work for functions on the unit sphere. Technically, our results are based on…

We consider temperate distributions on Euclidean spaces with uniformly discrete support and locally finite spectrum. We find conditions on coefficients of distributions under which they are finite sum of derivatives of generalized lattice…

We prove that if a family of metrics, $g_i$, on a compact Riemannian manifold, $M^n$, have a uniform lower Ricci curvature bound and converge to $g_\infty$ smoothly away from a singular set, $S$, with Hausdorff measure, $H^{n-1}(S) = 0$,…

We study almost-minimizers of anisotropic surface energies defined by a H\"older continuous matrix of coefficients acting on the unit normal direction to the surface. In this generalization of the Plateau problem, we prove almost-minimizers…

The aim of this note is to prove that almost-minimizers of the perimeter are Reifenberg flat, for a very weak notion of minimality. The main observation is that smallness of the excess at some scale implies smallness of the excess at all…

Let $S(z)$ be an absolutely convergent Dirichlet series with a bounded spectrum and only real zeros $a_n$, let $\mu$ be the sum of unit masses at points $a_n$. It is proven that the Fourier transform $\hat\mu$ in the sense of distributions…

Close to the origin, the nonlinear Klein--Gordon equations on the circle are nearly integrable Hamiltonian systems which have infinitely many almost conserved quantities called harmonic actions or super-actions. We prove that, at low…

In this paper, we study the existence and the concentration behavior of minimizers for $i_V(c)=\inf\limits_{u\in S_c}I_V(u)$, here $S_c=\{u\in H^1(\R^N)|~\int_{\R^N}V(x)|u|^2<+\infty,~|u|_2=c>0\}$ and…

We prove that area-minimizing submanifolds are not generically smooth, settling a conjecture of White that asks the generic smoothness of area-minimizing submanifolds. We furthermore establish a lower bound on the Hausdorff dimension of the…

We prove that finite perimeter subsets of $\mathbb{R}^{n+1}$ with small isoperimetric deficit have boundary Hausdorff-close to a sphere up to a subset of small measure. We also refine this closeness under some additional a priori integral…

In this short note, we extend the celebrated results of Tao and Vu, and Krishnapur on the universality of empirical spectral distributions to a wide class of inhomogeneous complex random matrices, by showing that a technical and…

We introduce a $\mathbb{Z}$--coefficient version of Guth's macroscopic stability inequality for almost-minimizing hypersurfaces. In manifolds with a lower bound on macroscopic scalar curvature, we use the inequality to prove a lower bound…

We prove that any length metric space homeomorphic to a 2-manifold with boundary, also called a length surface, is the Gromov-Hausdorff limit of polyhedral surfaces with controlled geometry. As an application, using the classical…

We establish a criterion on wrapped Floer homology of an exact Lagrangian sub- manifold in a Liouville domain, which ensures the almost-existence of Hamiltonian chords near a given energy level. To this purpose we introduce a relative…

In this paper, we establish new quantitative convergence bounds for a class of functional autoregressive models in weighted total variation metrics. To derive our results, we show that under mild assumptions, explicit minorization and…

We study global reflection symmetries of almost periodic functions. In the non-limit periodic case, we establish an upper bound on the Haar measure of the set of those elements in the hull which are almost symmetric about the origin. As an…

We consider a variant of Gamow's liquid drop model with an anisotropic surface energy. Under suitable regularity and ellipticity assumptions on the surface tension, Wulff shapes are minimizers in this problem if and only if the surface…

An approximation, in the sense of $\Gamma$-convergence and in any dimension $d\geq1$, of Griffith-type functionals, with $p-$growth ($p>1$) in the symmetrized gradient, is provided by means of a sequence of non-local integral functionals…

We prove that special functions of bounded deformation with small jump set are close in energy to functions which are smooth in a slightly smaller domain. This permits to generalize the decay estimate by De Giorgi, Carriero, and Leaci to…