Convex Surfaces (Dover Books on Mathematics) - Softcover

Herbert Busemann

Softcover

ISBN 10: 0486462439 ISBN 13: 9780486462431

Publisher: Dover, 2008

Synopsis

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.

Edition details

• Publisher: Dover
• Publication date: 2008
• Language: English
• ISBN 10: 0486462439
• ISBN 13: 9780486462431
• Binding: Paperback
• Number of pages: 208