# Convex surfaces. by Herbert Busemann

By Herbert Busemann

In this self-contained geometry textual content, the writer describes the most result of convex floor thought, offering all definitions and exact theorems. the 1st part makes a speciality of extrinsic geometry and purposes of the Brunn-Minkowski concept. the second one half examines intrinsic geometry and the conclusion of intrinsic metrics.
Starting with a quick evaluate 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 conception and its purposes is by means of examinations of intrinsic metrics, the metrics of convex hypersurfaces, geodesics, angles, triangulations, and the Gauss-Bonnet theorem. the ultimate bankruptcy explores the stress of convex polyhedra, the conclusion of polyhedral metrics, Weyl's challenge, neighborhood recognition of metrics with non-negative curvature, open and closed surfaces, and smoothness of realizations.

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