Vosughi-Oskui, Asghar (1989) Equichordality. University of Southampton, Doctoral Thesis.
Abstract
A subset S of Euclidean space cal En is said to be equichordal of gauge k if S is the locus of the end-points of a family of chords of length k all of which are aligned with a fixed point p of cal En, the fulcrum of S. The case where S is the image of a smooth immersion of a closed connected (n-1)-manifold is of particular interest. The main results are concerned with existence problems, the position of the fulcrum p in relation to S and its complement, questions of volume and area, symmetry phenomena, and medial behaviour. (DX89588)
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