Let X and Y be real normed spaces f : ? a surjective mapping. Then satisfies { ? ( x ) + y , ? } = ? if only is phase equivalent to linear isometry, that is, ? U where isometry 1 . This Wigner's type result for spaces.

A leaf of a compact foliated space has a well defined quasi-isometry type and it is a natural question to ask which quasi-isometry types of (intrinsic) metric spaces can appear as leaves of foliated spaces. There are two more or less related concepts of quasi-isometry. The first one is that used in Riemannian geometry, namely, two (Lipschitz) manifolds are quasi-isometric if there is a Lipschit...

\begin{abstract} Let $M$ be a complete Riemannian manifold and $G$ Lie subgroup of the isometry group acting freely properly on $M.$ We study Dirichlet Problem% \[ \left\{ \begin{array} [c]{l}% \operatorname{div}\left( \frac{a\left( \left\Vert \nabla u\right\Vert \right) }{\left\Vert }\nabla u\right) =0\text{ in }\Omega u|\partial\Omega=\varphi \end{array} \right. \] where $\Omega$ is $G-$invar...

For real hyperbolic spaces, the dynamics of individual isometries and the geometry of the limit set of nonelementary discrete isometry groups have been studied in great detail. Most of the results were generalised to discrete isometry groups of simply connected Riemannian manifolds of pinched negative curvature. For symmetric spaces of higher rank, which contain isometrically embedded Euclidean...