Table of contents

CONTENTS Introduction Part I. Geodesic flows § 1. Preliminary information from differential geometry, topology, and ergodic theory § 2. Local theory § 3. Hyperbolic properties of geodesic flows § 4. The axiom of visibility and the axiom of asymptoticity § 5. Limiting spheres § 6. Topological properties of geodesic flows § 7. Ergodic properties of geodesic flows § 8. Geodesic flows on manifolds of Anosov type Part II. Frame flows and horocycle flows § 9. Definition of a frame flow § 10. Topological and ergodic properties of a frame flow § 11. Definition of the horocycle flow § 12. Topological and ergodic properties of the horocycle flows References

CONTENTS Introduction § 1. Extremal plurisubharmonic functions and pluripolar sets in § 2. Plurimeagre sets in § 3. Pluriregularity of sets in § 4. Pluriregularity of polynomially convex compact sets § 5. The -measure and its properties § 6. The connection between an extremal function and the -measure § 7. The operator § 8. Maximal functions and their connection with the operator § 9. The capacitance of condensers and the solution of the first Lelong problem on a Stein manifold § 10. Further capacity characteristics of compact sets in § 11. The -measure of boundary sets and the generalized maximum principle for maximal functions § 12. Conclusion References

CONTENTS Introduction § 1. On spline functions § 2. Closures of sets of monosplines § 3. Theorems on zeros of monosplines § 4. Extremal properties of a monospline with multiple nodes § 5. Existence and structure of the optimal monospline § 6 Uniqueness of the optimal monospline § 7 On the best quadrature formulae § 8. On optimality of formulae of Euler-Mclaurin type Conclusion References