Viktor Schroeder

Manifolds of nonpositive curvature

Preface.-Introduction.-Lectures on Manifolds of Nonpositive Curvature.-Simply Connected Manifolds of Nonpositive Curvature.-Groups of Isometries.-Finiteness theorems.-Strong Rigidity of Locally Symmetric Spaces.-Appendix 1. Manifolds of Higher Rank.-Appendix 2: Finiteness Results for Nonanalytic Manifolds.-Appendix 3: Tits Metric and the Action of Isometries at Infinity.-Appendix 4: Tits Metric and Asymptotic Rigidity.-Appendix 5: Symmetric Spaces of Noncompact types.-References.-Subject Index.

Elements of Asymptotic Geometry

Asymptotic geometry is the study of metric spaces from a large scale point of view, where the local geometry does not come into play. An important class of model spaces are the hyperbolic spaces (in the sense of Gromov), for which the asymptotic geometry is nicely encoded in the boundary at infinity.   In the first part of this book, in analogy with the concepts of classical hyperbolic geometry, the authors provide a systematic account of the basic theory of Gromov hyperbolic spaces. These spaces have been studied extensively in the last twenty years, and have found applications in group theory, geometric topology, Kleinian groups, as well as dynamics and rigidity theory. In the second part of the book, various aspects of the asymptotic geometry of arbitrary metric spaces are considered. It turns out that the boundary at infinity approach is not appropriate in the general case, but dimension theory proves useful for finding interesting results and applications.   The text leads concisely to some central aspects of the theory. Each chapter concludes with a separate section containing supplementary results and bibliographical notes. Here the theory is also illustrated with numerous examples as well as relations to the neighboring fields of comparison geometry and geometric group theory.   The book is based on lectures the authors presented at the Steklov Institute in St. Petersburg and the University of Zurich. It addressed to graduate students and researchers working in geometry, topology, and geometric group theory.

Extensions of Lipschitz maps into Hadamard spaces

Abstract. We prove that every

Amenable Groups and Stabilizers of Measures on the Boundary of a Hadamard Manifold

\lambda

The fundamental group of compact manifolds without conjugate points

-Lipschitz map

Jung's Theorem for Alexandrov Spaces of Curvature Bounded Above

f : S \to Y

Quasi-metric and metric spaces

defined on a subset of an arbitrary metric space X possesses a

Codimension one tori in manifolds of nonpositive curvature

c \lambda

Rigidity of convex domains in manifolds with nonnegative Ricci and sectional curvature.

-Lipschitz extension

Perturbations of the harmonic map equation

\bar{f} : X \to Y