We consider asymptotically flat Riemannian manifolds with nonnegative scalar curvature that are conformal to Rn \ Ω, n ≥ 3, and so that their boundary is a minimal hypersurface. (Here, Ω ⊂ Rn is open bounded with smooth mean-convex boundary.) We prove that the ADM mass of any such manifold is bounded below by (V/βn) (n−2)/n, where V is the Euclidean volume of Ω and βn is the volume of the Eucli...

Let S be a closed orientable surface with genus g ≥ 2. For a sequence σi in the Teichmüller space of S, which converges to a projective measured lamination [λ] in the Thurston boundary, we obtain a relation between λ and the geometric limit of pants decompositions whose lengths are uniformly bounded by a Bers constant L. We also show that this bounded pants decomposition is related to the Gromo...

This paper studies regional boundary stabilization of nonlinear Schrödinger equation with state delay and bounded internal disturbance. The boundary constrained control law is designed by using the backstepping method. Regional input-tostate stability (ISS) of the perturbed system with time-delay is established by a Lyapunov function and a generalized Halanay’s inequality. Estimates on the set ...

The author deals with the quasilinear parabolic equation ut = [uα + g(u)]∆u + buα+1+f(u,∇u) with Dirichlet boundary conditions in a bounded domain Ω, where f and g are lower order terms. He shows that, under suitable conditions on f and g, whether the solution is bounded or blows up in a finite time depends only on the first eigenvalue of −∆ in Ω with Dirichlet boundary condition. For some spec...

A theorem of Gromov says that a complete finite volume Riemannian manifold of bounded negative curvature is the interior of a compact manifold with boundary. If, in addition, the curvature is bounded away from zero then the boundary is an aspherical manifold with virtually nilpotent fundamental group. I will discuss examples showing this is no longer true if the curvature is allowed to approach...

The tomographic imaging of vector elds on bounded domains is considered. Reconstruction formulas for the probe transform are rst shown to be valid on bounded domains. It is then shown that potential functions reconstructed from these formulas include a component that arises from the harmonic component of the vector eld, which is due to boundary conditions alone. Closed form expressions for the ...

We consider the stationary Stokes problem in a three-dimensional fluid domain F with non-homogeneous Dirichlet boundary conditions. We assume that this fluid domain is the complement of a bounded obstacle B in a bounded or an exterior smooth container Ω. We compute sharp asymptotics of the solution to the Stokes problem when the distance between the obstacle and the container boundary is small.

In this paper, we study the new subclasses of analytic functions in the unit disk E by using Carlson Shaffer operator and generalized Janowski functions. These new analytic classes relates with the concept of functions of bounded radius rotation and bounded Mocanu variation. Inclusion results and convolution invariant property are investigated.

We consider the stability in the inverse problem consisting in the determination of an electric potential q, appearing in a Dirichlet initial-boundary value problem for the wave equation ∂2 t u − ∆u + q(x)u = 0 in an unbounded wave guide Ω = ω × R with ω a bounded smooth domain of R2, from boundary observations. The observation is given by the Dirichlet to Neumann map associated to a wave equat...

In this paper, we investigate the existence of positive solutions for the ellipticequation $Delta^{2},u+c(x)u = lambda f(u)$ on a bounded smooth domain $Omega$ of $R^{n}$, $ngeq2$, with Navier boundary conditions. We show that there exists an extremal parameter$lambda^{ast}>0$ such that for $lambda< lambda^{ast}$, the above problem has a regular solution butfor $lambda> lambda^{ast}$, the probl...