SHORTEST CURVES IN JORDAN REGIONS VARY CONTINUOUSLY WITH THE BOUNDARY

Suppose a closed loop of wire in the plane defines a Jordan region, an d two points in the interior of that region are joined by a taut rubbe r band constrained to lie in the region by that wire boundary. Now sup pose that both the wire and the interior points are continuously pertu rbed (so that the perturbed endpoints lie in the interior of the pertu rbed Jordan region at each stage). Then the ruber band moves continuou sly. We provide a mathematical formulation and proof of this assertion . (C) 1994 Academic Press, Inc.