Convex Surfaces by Herbert Busemann
In this self-contained geometry text, the author describes the main results of convex surface theory, providing all definitions and precise theorems. The first half focuses on extrinsic geometry and applications of the Brunn-Minkowski theory. The second part examines intrinsic geometry and the realization of intrinsic metrics.Starting with a brief overview of notations and terminology, the text proceeds to convex curves, the theorems of Meusnier and Euler, extrinsic Gauss curvature, and the influence of the curvature on the local shape of a surface. A chapter on the Brunn-Minkowski theory and its applications is followed by examinations of intrinsic metrics, the metrics of convex hypersurfaces, geodesics, angles, triangulations, and the Gauss-Bonnet theorem. The final chapter explores the rigidity of convex polyhedra, the realization of polyhedral metrics, Weyl's problem, local realization of metrics with non-negative curvature, open and closed surfaces, and smoothness of realizations.
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Non-Euclidean Geometry
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A Geometric Introduction to Topology
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Fibonacci and Lucas Numbers, and the Golden Section
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Intriguing Mathematical Problems
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Calculus of Variations
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History of Mathematics: General Survey of the History of Elementary Mathematics v. 1
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Mathematical Puzzling
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Greek Mathematical Thought and the Origin of Algebra
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Introduction to Field Theory
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Introduction to Partial Differential Equations
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Modern Nonlinear Equations
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The Foundations of Statistics
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The Gamma Function
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The Mathematics of Games
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Structure of Algebras
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Numbers
Herbert Busemann (1905-1994) was one of the most original geometers of the twentieth century, and one of the main founders of metric methods in geometry. His work brought together the axiomatic geometry of Hilbert, Minkowski's work on convex bodies, and the differential geometry that had blossomed in the 1920s and 1930s - but that only caught up with his insistence on global results after the im grossem revolution of the 1960s. A geometer well ahead of his time, Busemann pioneered topics such as the theory of calibrations, global differential geometry and the geometry of normed spaces. His works are a gold mine of ideas and problems that will continue to influence research in convex and metric geometry. Busemann's originality is accompanied by a return to the sources, that is, to the most fundamental elements of geometry. The techniques he introduced and the problems he formulated have a considerable influence on modern research and seem poised to continue that influence well into the future.
| SKU | Unavailable |
| ISBN 13 | 9780486462431 |
| ISBN 10 | 0486462439 |
| Title | Convex Surfaces |
| Author | Herbert Busemann |
| Series | Dover Books On Mathematics |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Dover Publications Inc. |
| Year published | 2008-02-04 |
| Number of pages | 196 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |