Related papers: A Stefan-Sussmann theorem for normal distributions…

Static manifolds with boundary were recently introduced by Cruz and Vit\'orio in the context of the prescribed scalar curvature problem in a manifold with boundary with prescribed mean curvature. This kind of manifold is also interesting…

We consider random Hermitian matrices with independent upper triangular entries. Wigner's semicircle law says that under certain additional assumptions, the empirical spectral distribution converges to the semicircle distribution. We…

The matrix Schr\"odinger equation is considered on the half line with the general selfadjoint boundary condition at the origin described by two boundary matrices satisfying certain appropriate conditions. It is assumed that the matrix…

Recently we generalized Toponogov's comparison theorem to a complete Riemannian manifold with smooth convex boundary, where a geodesic triangle was replaced by an open (geodesic) triangle standing on the boundary of the manifold, and a…

We prove an abstract index formula about Sinnott's symbol between two different lattices. We also develop the theory of the universal distribution and predistribution in a double complex point of view. The theory of spectral sequence is…

For a homotopically energy-minimizing map $u: N^3\to S^1$ on a compact, oriented $3$-manifold $N$ with boundary, we establish an identity relating the average Euler characteristic of the level sets $u^{-1}\{\theta\}$ to the scalar curvature…

We prove the Bonnet theorem for statistical manifolds, which states that if a statistical manifold admits tensors satisfying the Gauss--Codazzi--Ricci equations, then it is locally embeddable to a flat statistical manifold (or a Hessian…

In this article we show the existence of limiting spectral distribution of a symmetric random matrix whose entries come from a stationary Gaussian process with covariances satisfying a summability condition. We provide an explicit…

We derive new bounds for the Castelnuovo-Mumford regularity of the ideal sheaf of a complex projective manifold of any dimension. They depend linearly on the coefficients of the Hilbert polynomial, and are optimal for rational scrolls, but…

Whereas subriemannian geometry usually deals with smooth horizontal distributions, partially hyperbolic dynamical systems provide many examples of subriemannian geometries defined by non-smooth (namely, H\"older continuous) distributions.…

In this paper we describe the propagation of smooth (C^\infty) and Sobolev singularities for the wave equation on smooth manifolds with corners M equipped with a Riemannian metric g. That is, for X=MxR, P=D_t^2-\Delta_M, and u locally in…

We investigate the Manakov model or, more generally, the vector nonlinear Schr\"odinger equation on the half-line. Using a B\"acklund transformation method, two classes of integrable boundary conditions are derived: mixed Neumann/Dirichlet…

For a stationary sequence that is regularly varying and associated we give conditions which guarantee that partial sums of this sequence, under normalization related to the exponent of regular variation, converge in distribution to a…

We study the asymptotic behaviour of the posterior distribution in a broad class of statistical models where the "true" solution occurs on the boundary of the parameter space. We show that in this case Bayesian inference is consistent, and…

Consensus algorithms are popular distributed algorithms for computing aggregate quantities, such as averages, in ad-hoc wireless networks. However, existing algorithms mostly address the case where the measurements lie in a Euclidean space.…

New bounds for the $k$-th order derivatives of the solutions of the normal and multivariate normal Stein equations are obtained. Our general order bounds involve fewer derivatives of the test function than those in the existing literature.…

We propose a Stein characterization of the Kummer distribution on (0, $\infty$). This result follows from our observation that the density of the Kummer distribution satisfies a certain differential equation, leading to a solution of the…

We prove the rigidity of rectifiable boundaries with constant distributional mean curvature in the Brendle class of warped product manifolds (which includes important models in General Relativity, like the deSitter--Schwarzschild and…

We discuss the notion of submanifolds with boundary with intrinsic $C^1$ regularity in sub-Riemannian Heisenberg groups and we provide some examples. Eventually, we present a Stokes' Theorem for such submanifolds involving the integration…

For the wave equation associated to the Laplacian on a compact manifold with boundary with a conic metric (with respect to which the boundary is metrically a point) the propagation of singularities through the boundary is analyzed. Under…