Sign-In
Cart
An Invitation to Alexandrov Geometry: Cat(0) Spaces
Paperback
Series: Lecture Notes in Mathematics, Book 2395
Currently unavailable to order
Please enter your email and a message will be sent to you when this product becomes available on our website.
ISBN10: 3032253489
ISBN13: 9783032253484
Publisher: Springer
Published: Aug 19 2026
Pages: 124
Language: English
ISBN13: 9783032253484
Publisher: Springer
Published: Aug 19 2026
Pages: 124
Language: English
This volume discusses CAT(0) spaces - metric spaces with nonpositive curvature in the sense of Alexandrov - which may be viewed as a non-linear generalization of Hilbert spaces. The book showcases the beauty and power of Alexandrov geometry by reaching interesting applications and theorems with a minimum of preparation.
This thoroughly revised and updated edition expands the 2019 SpringerBriefs in Mathematics volume. Drawing on extensive teaching experience, the authors have added two major topics, introduced numerous new exercises, corrected errors, simplified several proofs, and reorganized the material to better support teaching needs. The presentation is now more accessible and elementary. Primarily intended for graduate students and motivated undergraduates, the book includes numerous exercises ranging from routine to advanced, together with semisolutions and hints. It is well suited for self-study by advanced undergraduates, graduate students, and researchers. From the reviews of the first edition:
In the preface of this book, the authors state a Manifesto of Alexandrov geometry, under the slogan back to Euclid Alexandrov geometry may be viewed as a direct generalization of the axiomatic system of Euclid, with some of the equalities changed to inequalities. Indeed, metric geometry permits to formulate curvature bounds merely in terms of distance relations, e.g. via triangle comparison. This monograph is a brief and well crafted introduction into this highly active field. [...] Throughout the text there are numerous exercises of varying difficulty, as well as hints for the solutions in a separate section called Semisolutions. This book is a pleasure to read and is highly recommended as a concise and stimulating introduction to metric geometry.
Monatshefte für Mathematik 2021
In the preface of this book, the authors state a Manifesto of Alexandrov geometry, under the slogan back to Euclid Alexandrov geometry may be viewed as a direct generalization of the axiomatic system of Euclid, with some of the equalities changed to inequalities. Indeed, metric geometry permits to formulate curvature bounds merely in terms of distance relations, e.g. via triangle comparison. This monograph is a brief and well crafted introduction into this highly active field. [...] Throughout the text there are numerous exercises of varying difficulty, as well as hints for the solutions in a separate section called Semisolutions. This book is a pleasure to read and is highly recommended as a concise and stimulating introduction to metric geometry.
Monatshefte für Mathematik 2021
Also from
Alexander, Stephanie
Also in
Geometry
Oliver Byrne's Elements of Euclid: The First Six Books with Coloured Diagrams and Symbols (Art Meets Science Edition)
Art Meets Science
Hardcover
$59.99
The Little Book of Sacred Geometry: How to Harness the Power of Cosmic Patterns, Signs and Symbols
Carvel, Astrid
Paperback
$10.44
Math Fundamentals 3 - Geometry: For Middle School - A Quickstudy Laminated Reference Guide
Warren, Peggy
Wright, Susan
Expolog
Other
$6.60
6th and 7th Grade Math Workbook: Math Practice Book for Grade 6 and 7 [New Edition Includes 900] Practice Questions]
Apex Test Prep
Paperback
$19.49
Oliver Byrne's Elements of Euclid: The First Six Books with Coloured Diagrams and Symbols (Art Meets Science Edition)
Art Meets Science
Paperback
$47.49
Do Plants Know Math?: Unwinding the Story of Plant Spirals, from Leonardo Da Vinci to Now
Dumais, Jacques
Douady, Stéphane
Golé, Christophe
Hardcover
$26.55
Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everythingelse
Ellenberg, Jordan
Paperback
$18.05
Sacred Geometry (Conscious Guides): How to Use Cosmic Patterns to Power Up Your Life
Foster, Jemma
Paperback
$18.04
Geometría Y Trigonometría Baldor 4a. Ed. / Baldor's Geometry and Trigonometry, 4th Edition
Baldor, Aurelio
Hardcover
$29.40
Drawing Circle Images: How to Draw Artistic Symmetrical Images with a Ruler and Compass
Studio, Musigfi
Paperback
$8.63
Drawing Geometric Solids: How to Draw Polyhedra from Platonic Solids to Star-Shaped Stellated Dodecahedrons
Design, Sympsionics
Paperback
$12.38
Mathematics: Its Content, Methods and Meaning
Kolmogorov, A. N.
Lavrent'ev, M. a.
Aleksandrov, A. D.
Paperback
$61.75
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra
O'Shea, Donal
Cox, David A.
Little, John
Hardcover
$125.99
Make: Trigonometry: Build Your Way from Triangles to Analytic Geometry
Horvath, Joan
Cameron, Rich
Paperback
$28.49
College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle
Altshiller-Court, Nathan
Paperback
$17.05
Liberty's Grid: A Founding Father, a Mathematical Dreamland, and the Shaping of America
Alexander, Amir
Hardcover
$28.50
Geometry: 1001 Practice Problems for Dummies (+ Free Online Practice)
Kuang, Amber
Ma, Allen
Paperback
$66.50
4th Grade Math Workbook: 1500+ Practice Questions for Daily Exercise [Math Workbooks Grade 4]
Apex Test Prep
Paperback
$19.49
Amazing Patterns: Adult Coloring Book, Stress Relieving Mandala Style Patterns
Coloring Books for Adults
Adult Colouring Books
Adult Coloring Books
Paperback
$12.49
Tensor Calculus and Differential Forms: From Vector Calculus to the Geometry of Forms
Efthymiou, Thanasis
Hardcover
$28.49
The Fifth Postulate: How Unraveling a Two-Thousand-Year-Old Mystery Unraveled the Universe
Bardi, Jason Socrates
Hardcover
$26.55
Introduction to the Geometrical Foundations of General Relativity: A Compendium of Tensor Calculus
Wichmann, Bernd
Paperback
$24.64
A Geometric Analysis of the Platonic Solids and Other Semi-Regular Polyhedra
MacLean, Kenneth J. M.
Hardcover
$40.80
Functional and Harmonic Analysis: Weighted Lebesgue Spaces, Muckenhoupt Weights, Convexity and Bmo Spaces
Chaparro Gutiérrez, Héctor Camilo
Castillo, René Erlin
Ramos-Fernández, Julio César
Paperback
$73.14
How to Do Good Mathematics: Differential Geometry, Global Topology, and the Wisdom of a Wolf Prize Laureate
Chern, Shiing-Shen
Hardcover
$75.95