Birkhäuser-Verlag, Basel, 1997

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Table of Contents

1 Introduction

1.1 Examples of Riemannian manifolds of negative or nonpositive sectional curvature
      Appendix to §1.1: Symmetric spaces of noncompact type
1.2 Mordell and Shafarevitch type problems
1.3 Geometric superrigidity

2 Spaces of nonpositive curvature

2.1 Local properties of Riemannian manifolds of nonpositive sectional curvature
2.2 Nonpositive curvature in the sense of Busemann
2.3 Nonpositive curvature in the sense of Alexandrov

3 Convex functions and centers of mass

3.1 Minimizers of convex functions
3.2 Centers of mass
3.3 Convex hulls

4 Generalized harmonic maps

4.1 The definition of generalized harmonic maps
4.2 Minimizers of generalized energy functionals

5 Bochner-Matsushima type identities for harmonic maps and rigidity theorems

5.1 The Bochner formula for harmonic one-forms and harmonic maps
5.2 A Matsushima type formula for harmonic maps
5.3 Geometric superrigidity