Let X be a Hadamard manifold and let γ be an isometry on X. The function dγ on X defined by dγ(x): = d(x,γx) is called the di splacement function of γ. The displacement function dγ is convex, because d is convex on X × X.
KeywordsConvex Subset Displacement Function Hyperbolic Plane Geodesic Segment Nonpositive Curvature
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