Metric Spaces, Convexity and Nonpositive Curvature |
Contents
Preface | 1 |
Convexity in vector spaces | 5 |
2 | 7 |
Length spaces and geodesic spaces | 34 |
Notes on Chapter 2 | 77 |
Distances | 100 |
Convex functions | 161 |
Strictly convex normed vector spaces | 179 |
Notes on Chapter 8 | 204 |
Locally convex spaces | 211 |
Notes on Chapter 9 | 228 |
Isometries | 241 |
Busemann functions corays and horospheres | 261 |
| 275 | |
| 276 | |
| 283 | |
Other editions - View all
Metric Spaces, Convexity, and Non-positive Curvature Athanase Papadopoulos No preview available - 2014 |
Common terms and phrases
affine segment affinely reparametrized geodesic arbitrary points ball B(x Busemann space Chapter closed ball co-ray completes the proof consider contained converges convex functions convex subset Corollary covering map defined definition distance function distance-preserving endpoints equal equipped Euclidean space examples finite fixed point geodesic lines geodesic metric space geodesic path geodesic segment joining Hausdorff distance homeomorphism horospheres hyperbolic space implies infimum integer interval K-Lipschitz Lemma length metric length space let f let us prove local isometry locally compact locally convex map f map ƒ Menger neighborhood nonempty nonpositive curvature normed vector space notion obtain open ball parametrized by arclength path joining plane positive real number proof of Proposition properties pseudo-metric radius rectifiable paths reparametrized local geodesic respectively Riemannian manifolds sequence space and let strictly convex subdivision surface t₁ Teichmüller space Theorem topology triangle inequality uniquely geodesic space
References to this book
In the Tradition of Ahlfors-Bers, IV: Ahlfors-Bers Colloquium, May 19-22 ... Richard Douglas Canary No preview available - 2007 |
In the Tradition of Ahlfors-Bers, IV: Ahlfors-Bers Colloquium, May 19-22 ... Richard Douglas Canary No preview available - 2007 |