Total curvature and simple pursuit on domains of curvature bounded above

Details Total curvature and simple pursuit on domains of curvature bounded above Total curvature and simple pursuit on domains of curvature bounded above

2009-09-23

arxiv.org/abs/0909.4113v1

Mathematics

Metric Geometry

Scientific paper

We show how circumradius and asymptotic behavior of curves in CAT(0) and CAT(K) spaces(K>0) are controlled by growth rates of total curvature. We apply our results to pursuit and evasion games of capture type with simple pursuit motion, generalizing results that are known for convex Euclidean domains, and obtaining results that are new for convex Euclidean domains and hold on playing fields vastly more general than these.

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