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. 1958 edition. Reprint of the Interscience Publishers, Inc., New York, 1958 edition.
Convex Sets and Their Applications by Steven R. Lay Suitable for advanced undergraduates and graduate students, this text introduces characterizations of convex sets, polytopes, duality, optimization, and convex functions. Exercises include hints, solutions, and references. 1982 edition.
General Investigations of Curved Surfaces: Edited with an Introduction and Notes by Peter Pesic by Karl Friedrich Gauss, Adam Hiltebeitel, James Morehead, Peter Pesic This influential work defines the concept of surface curvature and presents the important theorem stating that the "Gauss curvature" is invariant under arbitrary isometric deformation of a curved surface. 1902 edition.
Geometry and Convexity: A Study in Mathematical Methods by Paul J. Kelly, Max L. Weiss This text assumes no prerequisites, offering an easy-to-read treatment with simple notation and clear, complete proofs. From motivation to definition, its explanations feature concrete examples and theorems. 1979 edition.
