Abstract In the context of control and estimation under information constraints, restoration entropy measures minimal required data rate above which state a system can be estimated so that quality does not degrade over time and, conversely, improved. The remote observer here is assumed to receive its through communication channel finite bit-rate capacity. this paper, we provide new characteriza...

We consider a periodic magnetic Schrödinger operator H, depending on the semiclassical parameter h > 0, on a noncompact Riemannian manifold M such that H(M,R) = 0 endowed with a properly discontinuous cocompact isometric action of a discrete group. We assume that there is no electric field and that the magnetic field has a periodic set of compact magnetic wells. We suppose that the magnetic fie...

For a smooth, compact Riemannian manifold (M, g) of dimension N ≥ 3, we are interested in the critical equation ∆gu+ ( N − 2 4(N − 1) Sg +εh ) u = u N+2 N−2 in M , u > 0 in M , where ∆g is the Laplace–Beltrami operator, Sg is the Scalar curvature of (M, g), h ∈ C (M), and ε is a small parameter.

We estimate the lower bound of the first Dirichlet eigenvalue of a compact Riemannian manifold with negative lower bound of Ricci curvature in terms of the diameter and the lower bound of Ricci curvature and give an affirmative answer to the conjecture of H. C. Yang for the first Dirichlet eigenvalue.

We estimate the lower bound of the first Dirichlet eigenvalue of a compact Riemannian manifold with negative lower bound of Ricci curvature in terms of the diameter and the lower bound of Ricci curvature and give an affirmative answer to the conjecture of H. C. Yang.

LetM be a smooth Riemannian manifold with the metric (gij) of dimension n, and let H = 1 2 g(q)pipj + V (t, q) be a smooth Hamiltonian on M, where gij is the inverse matrix of (gij). Under suitable assumptions we prove the existence of heteroclinic orbits of the induced Hamiltonian systems.

In this paper, we prove that the Ricci tensor of an almost Kenmotsu 3-h-manifold is cyclic-parallel if and only if it is parallel and hence, the manifold is locally isometric to either the hyperbolic space H3(−1) or the Riemannian product H2(−4)× R. c ©2016 All rights reserved.

The present paper is devoted to the problem of (local) geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on generic corank 1 distributions. Using Pontryagin Maximum Principle, we treat Riemannian and sub-Riemannian cases in an unified way and obtain some algebraic necessary conditions for the geodesic equivalence of (sub-)Riemannian metrics. In this way first we obtain a new...

The present paper is devoted to the problem of (local) geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on generic corank 1 distributions. Using Pontryagin Maximum Principle, we treat Riemannian and sub-Riemannian cases in an unified way and obtain some algebraic necessary conditions for the geodesic equivalence of (sub-)Riemannian metrics. In this way first we obtain a new...

For ??(0,2), U?C, and an instance h of the Gaussian free field (GFF) on U, ?-Liouville quantum gravity (LQG) surface associated with (U,h) is formally described by Riemannian metric tensor e?h(dx2+dy2) U. Previous work authors showed that one can define a canonical (distance function) Dh U ?-LQG surface. We show this conformally covariant in sense it respects coordinate change formula for surfa...