On certain minimum problems in the theory of convex curves

Abstract

Introduction. In Chapter I we describe a set of eight related problems. Solutions of five of these problems are known. Solutions for two of the remaining three problems are given in Chapters VI and VIII, and a partial solution of the third is given in Chapter IX. The general method of attack is developed in Chapters III and IV. This method centers around a process whereby a plane convex body is asymmetrized into one of a set of associated bodies called triarcs. If difficulties occur in reading Chapter I, it is suggested that Chapter II be read first. Background material not found in the latter chapter is to be found in the well known book Theorie der konvexen KYrper by Bonnesen and