Rigidity of compact ideal boundaries of manifolds joined by Hausdorff approximations

The concept of ideal boundary of Hadamard monifolds was introduced by Eberlein and O\u27Neill [3] in 1973, which had marked a millestone is the study of the geometry of noncompact Reimannian manifolds. Since then, it has been utilized in various fields of research on Hadamard manifolds. ..

Total excess and Tits metric for piecewise Riemannian 2-manifolds

AbstractA piecewise Riemannian 2-manifold is a combinatorial 2-manifold with a triangulation such that each 2-simplex is a geodesic triangle of some Riemannian 2-manifold. In this paper, we study the total excess e(X) of a simply connected nonpositively curved piecewise Riemannian 2-manifold X in connection with the Tits metric on the boundary at infinity X(∞)