Related papers: Hyper contractivity on the unit circle for ultrasp…

We study the log-concave measures, their characterization via the Pr\'ekopa-Leindler property and also define a subset of it whose elements are called super log-concave measures which have the property of satisfying a logarithmic Sobolev…

Contractive coupling rates have been recently introduced by Conforti as a tool to establish convex Sobolev inequalities (including modified log-Sobolev and Poincar\'{e} inequality) for some classes of Markov chains. In this work, we show…

We introduce the boolean convolution for probability measures on the unit circle. Roughly speaking, it describes the distribution of the product of two boolean independent unitary random variables. We find an analogue of the characteristic…

We consider the multidimensional inverse problem of determining the conductivity coefficient of a hyperbolic equation in an infinite cylindrical domain, from a single boundary observation of the solution. We prove H{\"o}lder stability with…

We prove an estimate for arbitrary measure of sections of convex bodies. The proof is based on a stability result for intersection bodies.

We propose a unified description for the constants of motion for superintegrable deformations of the oscillator and Coulomb systems on N-dimensional Euclidean space, sphere and hyperboloid. We also consider the duality between these…

In contact geometry, a systolic inequality is a uniform upper bound on the shortest period of a closed Reeb orbit, in terms of the contact volume. We prove a general systolic inequality valid on Seifert bundles with non-zero Euler number…

This survey explores the foundational theory and recent developments in the study of hyperuniformity. We present a comprehensive mathematical framework in the context of weakly stationary random measures, emphasizing spectral…

This paper studies length estimates for trajectories on flat cone surfaces in terms of their self-intersection numbers. For an area-one flat cone surface, we obtain a lower bound for the length of a trajectory, with constants depending only…

For $C^{1+}$ maps, possibly non-invertible and with singularities, we prove that each homoclinic class of an ergodic adapted hyperbolic measure carries at most one adapted hyperbolic measure of maximal entropy. We then apply this to study…

We derive an optimal bound on the sum of entropic uncertainties of two or more observables when they are sequentially measured on the same ensemble of systems. This optimal bound is shown to be greater than or equal to the bounds derived in…

The equivalence between logarithmic Sobolev inequalities and hypercontractivity of solutions of Hamilton-Jacobi equations has been proved in [5]. We consider a semi-Lagrangian approximation scheme for the Hamilton-Jacobi equation and we…

In this paper we extend the local scalar curvature rigidity result in [6] to a small domain on general vacuum static spaces, which confirms the interesting dichotomy of local surjectivity and local rigidity about the scalar curvature in…

Complete hyperbolicity of small Euclidean balls with respect to a C^1-smooth almost complex structure standard at origin is improved to give a complete hyperbolicity of strictly pseudoconvex domains. More precise (and lower) regularity…

A positive representation for a set of complex densities is constructed. In particular, complex measures on a direct product of U(1) groups are studied. After identifying general conditions which such representations should satisfy, several…

We give precise estimates of some holomorphically invariant infinitesimal metrics near a pseudoconcave points in a wide family of ``model'' domains for that situation in $\mathbb C^2$. This extends to metrics (rather distances) the authors'…

We provide an elementary proof of the equivalence of various notions of uniform hyperbolicity for a class of $\mathrm{GL}(2,\mathbb{C})$ cocycles and establish a Johnson-type theorem for extended CMV matrices, relating the spectrum to the…

We consider the local dimension spectrum of a weak Gibbs measure on a C^1 non-uniformly hyperbolic system of Manneville- Pomeau type. We present the spectrum in three ways: using invariant measures, uniformly hyperbolic ergodic measures and…

This paper deals with the invariance of a measure on Sobolev spaces of low regularity under the flow of the cubic non linear wave equation on the unit ball of 3 under the assumption of spherical symmetry. It presents two aspects, an…

We give a sharp convexity estimate for L-functions which have a functional equation and an Euler product.