The ideal boundaries of complete open surfaces
The ideal boundary with Tits metric of a Hadamard manifold has been defined by Gromov as the set of equivalence classes of rays with respect to the asymptotic relation. Here the non-positivity of the sectional curvature is essential to construct the ideal boundary. Nevertheless, in the present paper, we construct the ideal boundary with Tits metric of a finitely connected, oriented, complete and open surface by a new equivalence relation between rays through the existence of the total curvature of the surface. This ideal boundary has many natural geometric properties analogous to the case of the standard flat cone provided the surface has only one end.
scientific article; zbMATH DE number 4153385
scientific article