Etudes Scientiflques. He is a member of the French Academy of Sciences and a foreign member of the U.S. National Academy of Sciences. His witty one-liners served as starting points of Ph.D theses, his short comments and exercises has grown to excellent papers of various mathematicians. He created concepts like word hyperbolic groups, pseudoholomorphic curves, simplicial volume and many others. The goal of this essay is to ofier a sort of introduction to some of Gromov’s results and concepts.

1. Basic definitions, examples, and problems. 1.1. Symplectic forms and manifolds. An exterior differential 2-form w o n a smooth manifold V is called nonsingular if the associated homomorphism… Expand

We give an upper bound for the Betti numbers of a compact Riemannian manifold in terms of its diameter and the lower bound of the sectional curvatures. This estimate in particular shows that most… Expand

SummaryWe show in this paper that for everyn≧4 there exists a closedn-dimensional manifoldV which carries a Riemannian metric with negative sectional curvatureK but which admits no metric with… Expand

Length Structures: Path Metric Spaces.- Degree and Dilatation.- Metric Structures on Families of Metric Spaces.- Convergence and Concentration of Metrics and Measures.- Loewner Rediscovered.-… Expand