Asymptotic rigidity of Hadamard 2-spaces

Abstract

We classify locally compact, geodesically complete, 2-dimensional Hadamard spaces whose Tits ideal boundaries have the minimal diameter $\pi$. Furthermore, we classify the universal covering spaces of certain 2-dimensional nonpositively curved spaces, which is an extension of the result obtained in the polyhedral case by W. Ballmann, M. Brin, and S. Barré.