On the Possibility of Joining Two Pairs of Points in Convex Domains Using Paths

This article is devoted to the possibility of joining of two pairs of points of a convex domains by curves. We are interested in the case when these curves are not farther from each other than the distance between their end points, possibly, up to some absolute multiplicative constant. We have obtained some upper and lower bounds for the modulus of families of paths joining curves mentioned above.