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Download E-books Convex Surfaces (Dover Books on Mathematics) PDF

By Herbert Busemann

In this self-contained geometry textual content, the writer describes the most result of convex floor idea, delivering all definitions and detailed theorems. the 1st part specializes in extrinsic geometry and functions of the Brunn-Minkowski idea. the second one half examines intrinsic geometry and the conclusion of intrinsic metrics.
Starting with a quick evaluation of notations and terminology, the textual content proceeds to convex curves, the theorems of Meusnier and Euler, extrinsic Gauss curvature, and the impact of the curvature at the neighborhood form of a floor. A bankruptcy at the Brunn-Minkowski thought and its purposes is via examinations of intrinsic metrics, the metrics of convex hypersurfaces, geodesics, angles, triangulations, and the Gauss-Bonnet theorem. the ultimate bankruptcy explores the pressure of convex polyhedra, the belief of polyhedral metrics, Weyl's challenge, neighborhood awareness of metrics with non-negative curvature, open and closed surfaces, and smoothness of realizations.

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