## Abstract

In this paper, using the generalized version of the theory of combinatorial harmonic maps, we give a criterion for a finitely generated group Γ to have the fixed-point property for a certain class of Hadamard spaces, and prove a fixed-point theorem for random-group actions on the same class of Hadamard spaces. We also study the existence of an equivariant energy-minimizing map from a Γ-space to the limit space of a sequence of Hadamard spaces with the isometric actions of a finitely generated group Γ. As an application, we present the existence of a constant which may be regarded as a Kazhdan constant for isometric discrete-group actions on a family of Hadamard spaces.

Original language | English |
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Pages (from-to) | 363-379 |

Number of pages | 17 |

Journal | Annals of Global Analysis and Geometry |

Volume | 35 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2009 Jun |

Externally published | Yes |

## Keywords

- Finitely generated group
- Fixed-point property
- Hadamard space
- Harmonic map
- Random group
- Rigidity

## ASJC Scopus subject areas

- Analysis
- Political Science and International Relations
- Geometry and Topology