We prove that any nonelementary geometrically finite group of isometries of a pinched Hadamard manifold has nonzero algebraic entropy in the sense of M. Gromov. In other words it has uniform exponential growth.

In this paper we construct and study isoperimetric functions at infinity for Hadamard manifolds. These quasi-isometry invariants give a measure of the spread of geodesics in such a manifold.

In 1975, Yau [Y] proved, by way of a gradient estimate, that a complete manifold M with non-negative Ricci curvature must satisfy the strong Liouville property for harmonic functions. The strong Liouville property (Liouville property) asserts that any positive (bounded) harmonic function defined on M must be identically constant. In 1980, Cheng [C] generalized the gradient estimate to harmonic ...

Let M a Riemannian manifold of dimension m ≥ 3, let Σ be a closed smooth submanifold of M of co-dimension at least 2, and let H be a Hadamard manifold with pinched sectional curvatures. We prove the existence and uniqueness of harmonic maps φ : M \ Σ → H with prescribed singularities along Σ. When M = R, and H = H C , the complex hyperbolic space, this result has applications to the problem of ...

We discuss the conformal boundary of a warped product of two length spaces and provide a method to calculate this in terms of the individual conformal boundaries. This technique is then applied to produce CAT(0)-spaces with complicated conformal boundaries. Finally we prove that the conformal boundary of an Hadamard n-manifold is always simply connected for n ≥ 3, thus providing a bound for the...

— We study the local existence of strong solutions for the cubic nonlinear wave equation with data in H(M), s < 1/2, where M is a three dimensional compact riemannian manifold. This problem is supercritical and can be shown to be strongly ill-posed (in the Hadamard sense). However, after a suitable randomization, we are able to construct local strong solution for a large set of initial data in ...

In this thesis we investigate the existence of complex-valued harmonic morphisms on Lie groups and homogeneous Hadamard manifolds. The Lie groups that we are interested in have a particular decomposition of their Lie algebra. This decomposition allows us to define harmonic morphisms to R, n ≥ 2. Any homogeneous Hadamard manifold is isometric to a solvable Lie group S with a left-invariant metri...

Abstract: Completing the results achieved in a previous paper, we prove the symmetry of Hadamard/Seeley-deWitt off-diagonal coefficients in smooth D-dimensional Lorentzian manifolds. To this end, it is shown that, in any Lorentzian manifold, a sort of “local Wick rotation” of the metric can be performed provided the metric is a locally analytic function of the coordinates and the coordinates ar...

The aim of this note is to give a sufficient condition for pairs functions have convex separator when the underlying structure Cartan–Hadamard manifold, or more generally: reduced Birkhoff system. Some exotic behavior hulls are also studied.

We use the auxiliary principle technique to suggest and analyze a proximal point method for solving the mixed variational inequalities on the Hadamard manifold. It is shown that the convergence of this proximal point method needs only pseudomonotonicity, which is a weaker condition than monotonicity. Some special cases are also considered. Results can be viewed as refinement and improvement of ...