Vol. 43, No. 3, 1972

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Cut loci of points at infinity

George M. Lewis

Vol. 43 (1972), No. 3, 675–690

In a G-space R if B is a co-ray to A then the union of all co-rays to A that contain B is either a straight line or a co-ray to A maximal in that it is properly contained in no other co-ray to A. In the latter case, the initial point of the maximal co-ray is a copoint to A. The concept of co-point is an analogue to that of minimum point in a sense made precise. On certain non-compact G-surfaces of finite connectivity, including those with non-positive curvature, we characterize the locus of co-points to a given ray and obtain bounds for the number of components of this locus, the number of co-rays emanating from a co-point and the number of co-points that are origins of more than two co-rays.

Mathematical Subject Classification 2000
Primary: 53C70
Secondary: 53C20
Received: 14 September 1971
Published: 1 December 1972
George M. Lewis